http://wiki.superliminal.com/api.php?action=feedcontributions&user=Blobinati&feedformat=atomSuperliminal Wiki - User contributions [en]2022-09-28T12:51:13ZUser contributionsMediaWiki 1.25.1http://wiki.superliminal.com/index.php?title=Canonical_Moves&diff=3538Canonical Moves2022-09-24T21:20:30Z<p>Blobinati: </p>
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<div>If you were handed a physical 2x2x2x2 without explanation, it is not obvious how you would turn it as a puzzle. This is why the official canonical moveset exists. These are comprised of the basic moves that the community agrees on. Only these moves can be used for official solutions in the Hall of Fame. <br><br />
Watch [[https://www.youtube.com/watch?v=DzRH8BOJL8Q Melinda's video]] for a detailed overview.<br />
<br />
=History=<br />
[[File:2222rotating.png|thumbnail|left|200px|The original diagram]]<br />
Before the first prototype of the 2^4 was made, Melinda's diagram (at left) showed the simple rotations of the puzzle. It was obvious that you could rotate those 2 sides in any way you wanted. Gradually, through mailing list community consensus, the move set was narrowed down to just a couple of moves, plus a gyro. These moves are listed below. <br><br />
The canonical moves don't include some moves that are easy to show their relationship to the virtual puzzle. For example, a Ux2 move maps to the physical puzzle in a fun way, but isn't included. Check out [[https://www.youtube.com/watch?v=wwwEUH_dfs4|Rowan's video]] to see some extra moves that could theoretically be included in the future.<br />
<br />
=Canonical Moves=<br />
<br />
==Simple Rotation==<br />
You can 4D rotate the puzzle by rotating the cubic halves along each other symmetrically, such that the puzzle state stays the same. However, this does not allow you to reach every orientation of the puzzle. The gyro algorithm is necessary for reaching the rest of the orientations.<br />
<br />
==Cube cell turns==<br />
<br />
You can rotate the 2 cubic cells in any way you want, as this corresponds perfectly with rotating them on the physical puzzle. Melinda's video calls this an "arbitrary half puzzle juxtaposition". <br><br />
The notation for these moves is to use the Rubik's Cube notation with x, y, & z rotations. x goes in the same direction as R, y is like U, and z is like F. Any reorientation is generally considered to be 1 move. For example, doing Rx,y2 would be 1 move.<br />
<br />
==Long cell turns==<br />
From the horizontal position, the long cells are the U, F, D, & B cells. They can be twisted as if they were the sides of a 2x2x4 cuboid. These moves are notated U2, F2, D2, or B2. Technically their rotational plane should be specified more, as on the virtual puzzle, U2 could mean Ux2, Uy2, or Uz2. However, only one of these twists is canonical for each side. These are Uy2, Fz2, Dy2, and Bz2.<br />
<br />
==Gyro==<br />
<br />
[[File:GyroGif.gif|thumbnail|left|300px|One possible gyro algorithm]]<br />
In order to access full turns of other sides, it is needed to 4 dimensionally rotate the puzzle in such a way that the x axis stickers change. This is called a "gyro". There are many possible gyro algorithms, all of which have to use some sort of illegal (non-canonical) twist at some point. Watch [[https://www.youtube.com/watch?v=d2Fh_1m0UVY Melinda's video]] on gyro algorithms. <br><br />
"The gyro basically rapidly disassembles and reassembles the puzzle in the same state but rotated 4 dimensionally" - [[Markk's Physical Puzzles|Markk]]</div>Blobinatihttp://wiki.superliminal.com/index.php?title=File:2222rotating.png&diff=3537File:2222rotating.png2022-09-24T21:04:39Z<p>Blobinati: </p>
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<div></div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_2%5E4_Records&diff=3535Physical 2^4 Records2022-09-19T21:19:10Z<p>Blobinati: </p>
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<div>This page contains the unofficial records for timed speed solves of Melinda's Physical 2x2x2x2. Add your accomplishments to the tables below, following the existing patterns. You are honor bound to be accurate in your claims. Please add a link to your solve video. <br><br />
<br />
"Official" Regulations: <br><br />
<ul><br />
<li>You must use the official [[https://www.youtube.com/watch?v=DzRH8BOJL8Q canonical moveset]]. (Which is currently kind of disputed, but maybe we'll figure it out one day lol)</li><br />
<li>You are allowed to gyro and do 4D rotations during inspection</li><br />
<li>If piece(s) fall out accidentally, you may replace them, not worrying about if you put them back the wrong way or not. Then you are allowed to fix any weird errors due to that during the solve</li><br />
<li>If you do an illegal move, such as a single endcap 90 degree twist, you are allowed to fix it. (Just like being able to untwist a corner)</li><br />
</ul><br />
<br />
<br />
<br /><br />
<center><br />
{|border="1" cellpadding="5"<br />
|-<br />
!colspan="9"|<big>Official Records</big><br />
|-<br />
!colspan="3"|Two Handed<br />
!colspan="3"|One Handed<br />
!colspan="3"|BLD<br />
|-<br />
!Date||Name||Time||Date||Name||Time||Date||Name||Time<br />
|-<br />
|2019/8/11||Connor Lindsay||[[https://www.youtube.com/watch?v=oEdrWPEsKPQ 2:26]]<br />
|2022/07/31||Rowan Fortier||[[https://www.youtube.com/watch?v=ClqLrac3Ib4 6:25.12]] <br />
|2022/08/08||Asa Kaplan||[[https://www.youtube.com/watch?v=lBssOimXaFE 47:14]]<br />
|-<br />
|2021/11/15||Rowan Fortier||[[https://youtu.be/mgfhSL2fi7E 2:16.538]]<br />
|-<br />
|2021/12/6||Rowan Fortier||[[https://youtu.be/tOaBQs34oB0 2:05.27]]<br />
|-<br />
|2021/12/9||Rowan Fortier||[[https://youtu.be/I9hnsif4ImE 2:03.582]]<br />
|-<br />
|2021/12/11||Rowan Fortier||[[https://youtu.be/2SWo0zMlg8I 2:00.656]]<br />
|-<br />
|2021/12/11||Rowan Fortier||[[https://youtu.be/JJPJ7hgNLJU 1:56.748]]<br />
|-<br />
|2022/05/07||Rowan Fortier||[[https://youtu.be/RuUc26S5xpw 1:46.24]]<br />
|-<br />
|2022/06/20||Rowan Fortier||[[https://youtu.be/FSpuv9FJorw 1:28.14]]<br />
|-<br />
|2022/08/02||Rowan Fortier||[[https://youtu.be/XDW7wi4ryPE 1:27.17]]<br />
|-<br />
|2022/08/07||Grant S||[[https://www.youtube.com/watch?v=uEnk2yrJN7I 1:23.28]]<br />
|-<br />
|2022/08/12||Grant S||[[https://www.youtube.com/watch?v=X_FY-CUfvUI 1:07.57]]<br />
|-<br />
|2022/09/18||Grant S||[[https://www.youtube.com/watch?v=_qqXVKOVkAI 1:06.04]]<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<center><br />
{|border="1" cellpadding="5"<br />
|-<br />
!colspan="5"|<big>Unnofficial Records</big><br />
|-<br />
!Date||Name||Time||Type||Comments<br />
|-<br />
| ||Rowan Fortier||1:11.17||Speed||PB but not WR<br />
|-<br />
|2022/08/15||William Jestin Palmer||2:12.69||Speed||New Zealand Record<br />
|}</div>Blobinatihttp://wiki.superliminal.com/index.php?title=Main_Page&diff=3496Main Page2022-09-15T18:41:19Z<p>Blobinati: </p>
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<div>==MagicCube4D==<br />
[[File:classic-hypercube.png|thumbnail|left|350px|MagicCube4D]]<br />
<br /><br />
<big>'''MagicCube 4D'''</big><br />
[http://www.superliminal.com/cube/cube.htm]<br />
<br />
For the the 4-dimensional cube puzzle accomplishments, records, and documentation, see [[MagicCube4D]].<br />
<br> <br /><br />
<big>'''Records (first and shortest)'''</big><br />
<br />
For First and Shortest check [[MC4D_Records]].<br />
<br> <br /><br />
<big>'''Gallery'''</big><br />
<br />
Check amazing pictures in [[Image_gallery]].<br />
<br><br/><br />
<big>'''Solutions'''</big><br />
<br />
Solving tips and ideas for other solutions for 4D puzzles click [[MC4D_Solutions]].<br />
<br><br/><br />
<big>'''Join this wiki community'''</big><br />
<br />
To participate in wiki editing, [[Create_Account|create an account]].<br />
<br> <br /><br />
<br> <br /><br />
<br />
==MagicTile==<br />
[[File:MagicTile.PNG|thumbnail|left|350px|MagicTile]]<br />
<br />
<br /><br />
<big>'''MagicTile V2'''</big><br />
[http://www.roice3.org/magictile/]<br />
<br /><br /><br />
<big>'''Records (first and shortest)'''</big><br />
<br /><br />
For First and Shortest check [[MagicTile_Records]].<br />
<br><br /> <br />
<big>'''List of Solvers'''</big><br />
<br /> <br />
For MagicTile v2 Solutions check [[MagicTile v2 Solutions]].<br />
<br> <br /><br />
<big>'''Mathologer Challenge'''</big><br />
<br /> <br />
See the first 100 solvers of the Klein Bottle Rubik's Analogue [[http://roice3.org/magictile/mathologer/ here]].<br />
<br> <br /><br />
<br />
<big>'''Tips and ideas</big><br />
<br /> <br />
For solving tips and ideas for MagicTile puzzles click [[MagicTile aspects]].<br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br />
==Magic Puzzle Ultimate==<br />
[[File:MPUlt_v0.3.PNG|thumbnail|left|350px|Magic Puzzle Ultimate]]<br />
<br />
<br /><br />
<big>'''Magic Puzzle Ultimate'''</big><br />
[http://cardiizastrograda.com/astr/MPUlt/]<br />
<br />
<br /><br />
<big>'''Records (first and shortest)'''</big><br />
<br />
For First and Shortest check [[MPUlt_Records]].<br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br />
==Blindfolded Solving==<br />
[[File:BLD.PNG|thumbnail|left|350px|Blindfolded solving]]<br />
<br />
<br /><br />
<big>'''Rules'''</big><br />
<br /><br />
<br />
<big>The rule of a blindfolded solution without macros:</big><br />
<br /><br />
(1) Starting the solve: make a full scramble using any simulator.<br /><br />
(2) Memorization: the solver memorizes the puzzle without making any twist. The solver may change the viewpoint to inspect the whole puzzle. The solver must not take notes (per WCA regulations). <br /><br />
(3) Put on "blindfold": Preferences > Modes > Blindfold <br /><br />
(4) During the solve: now the solver may make twists.<br /><br />
(5) Ending the solve: a successful solution ends automatically. The duration of the solution includes both the memorization phase and the solving phase.<br />
<br /><br />
<br />
<big>The rule of a blindfolded solution with macros:</big> <br />
<br /><br />
As same as the rule without macros, except: before step (1) the solver may define macros, and during step (4) the solver may use the predefined macros.<br />
<br />
<br /><br />
<br />
<big>'''Records'''</big><br />
<br /><br />
Check [[BLD_Records]].<br />
<br />
<br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br />
==Permutations==<br />
[[File:MC7Dimage.PNG|thumbnail|left|350px|MagicCube7D]]<br />
<br />
<br /><br />
<big>'''Puzzle Index'''</big><br />
<br />
Find permutation counts of every puzzle with explanations in [[Permutations_Index]].<br />
<br> <br /><br />
<big>'''Notation'''</big><br />
<br />
For a description of the notation used in the permutation count explanations, visit [[Permutations_Notation]].<br />
<br/><br />
<br> <br/><br />
<br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br />
==Physical Puzzle==<br />
[[File:Physical3333.jpg|thumbnail|left|350px|Grant's Physical 3x3x3x3]]<br />
<br> <br/><br />
<br />
<big>'''History''' </big> <br><br />
Ever since the virtual hypercube programs were invented, people have wanted [[Physical Puzzle]]s to actually play with in real life. The first one of these was Melinda Green's Physical 2x2x2x2, conceptualized in 2014 and mass produced in 2021. By far the most popular puzzle (due to only 1 of each of the other puzzles existing đź’€), people speedsolve it. Check out these links below for more information: <br><br />
<br />
For different solving methods, visit [[Physical 2^4 Methods]]. <br><br />
For speedsolving records, visit [[Physical 2^4 Records]], but make sure to be familiar with the [[Canonical Moves]] first.<br />
<br />
<br> <br/><br />
<br />
<big>'''Grant's Puzzles''' </big><br />
<br><br/><br />
Grant designed and 3D printed his own puzzles based on Melinda's 2x2x2x2 piece design. He made a 2x2x2x3, 2x2x3x3, 3x3x3x2, and the holy grail, the 3x3x3x3.<br />
For more information on Grant's puzzles, visit [[Grant's Physical 4d Puzzles]]</div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_Puzzle&diff=3494Physical Puzzle2022-09-15T06:03:18Z<p>Blobinati: </p>
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<div><br />
== Definition ==<br />
In the context of hypercubing, a physical puzzle refers to an N+1 dimensional puzzle projected in N dimensions, such that the projection is operationally equivalent, i.e. the projection "emulates" the true puzzle. Usually, if not specified, it is used to refer to a 4D puzzle projected in 3D.<br />
<br />
== 2D Physical Puzzles ==<br />
<br/><br />
[[File:2d_physical_puzzles_v2.png|500px|thumb|left|Drawing showing (from top to bottom, left to right)2^3, 2x2x3, 2x3x3, 3^3, 2x2 pyraminx, 3x3 pyraminx, bandaged 3x3 pyraminx, bandaged 4x4 pyraminx]]<br />
<br />
When designing 3D physical puzzles, it's a good idea to try and step down the problem by first looking at what the 2D physical analog would look like. For example, the 2^3, or by it's more recognizable name, the 2x2x2, can be projected down into 2D by splitting it in 2 halves and putting them next to each other along the X or Y axis. By doing this, the Z axis will coincide with the X or the Y axis, which will make certain moves inaccessible without the use of a gyro algorithm to reorient the puzzle (the gyro algorithm does a cube rotation). We can also see that the projected cubies aren't square shaped, and that is because a square doesn't have 3 fold symmetry. <br><br />
<br />
By the same logic, we can then build a 3D physical 2^4/2x2x2x2 - split the hypercube in 2 halves and put them next to each other along X, Y or Z axis, making certain moves inaccessible without the use of a gyro. We can see that the 2^4 can have the cubies be cube shaped because (by mathematical coincidence) a cube has 4 fold symmetry (a 2^4 cubie has 4 colors). <br><br />
<br />
Another thing to note is that physical puzzles don't have a true mechanism/way to hold the pieces together, so magnets are used to hold the puzzle together. Because we don't have a true mechanism, we need to limit the moves we are allowed to do by the canonical moves to make sure we aren't doing illegal moves on the puzzle. <br><br />
<br />
Another example is the 3x3 pyraminx. In this case we can take a top-down orthographic view of the puzzle and then project it, making sure each piece type has the same shape in the projection so they are interchangeable. Doing this, we get an interesting 2D physical puzzle that looks like the wireframe of a tetrahedron projected in 2D, but with some of the lines disconnected. This is because we can't project a tetrahedron into 2D without unevenly distorting the shape or without having breaks in the shape. This can then be scrambled and solved using its canonical moves (rotate 3C pieces with its 2Cs, by first making sure all its associated 2Cs are touching it). By the same logic one can construct a 3D physical simplex.<br />
[[File:2d_pyraminx_wireframe.png|thumb|right|Image showing the correlation between the top down orthographic view of the pyraminx, the 2D physical pyraminx and the wireframe of the pyraminx]]<br />
<br />
<br/><br />
== 3D Physical Puzzles ==<br />
<br/><br />
[[File:1080p_3d_physical_puzzles_v2.png|thumb|left|500px|Render showing (from left to right, top to bottom) Bandaged void simplex, simplex, 1x2x2x2, 1x3x3x3, 2^4, 2x2x2x3, 2x2x3x3, 2x3x3x3, 3^4]]<br />
The first physical puzzle was the [[2^4]], designed by Melinda Green in 2017. After this [[Grant's Physical 4d Puzzles|Grant]], Luna, Hactar and [[Markk's Physical Puzzles|Markk]] designed and built many other 3D physical puzzles based on Melinda's 2^4 design, like the 3^4, the simplex, and hypercuboids like the 2x2x3x3. There where attempts at designing shapeshifting physical puzzles with no success.<br />
<br />
== 3D Physical designs list ==<br />
Below is a table of physical puzzles, both produced and unproduced. <br><br />
<br />
<center><br />
{|border="1" cellpadding="5"<br />
|-<br />
!colspan="3"|<big>Real Physical Puzzles</big><br />
|-<br />
!Puzzle||Name(s)||Date Finished<br />
|-<br />
|2x2x2x2||Melinda Green||2017<br />
|-<br />
|2x2x2x3||Luna & Grant||December 2021<br />
|-<br />
|2x2x3x3||Grant & Hactar||May 2022<br />
|-<br />
|2x3x3x3||Grant||July 2022<br />
|-<br />
|3x3x3x3||Grant||July 2022<br />
|-<br />
!colspan="3"|<big>Unmade Physical Puzzles</big><br />
|-<br />
!Puzzle||Name(s)||Date of thought<br />
|-<br />
|1x1xnxn series||Grant||<br />
|-<br />
|Simplex||Markk||August 2022<br />
|-<br />
|pretty much any cuboid||Grant||<br />
|}<br />
<br />
<br />
== Physical Shapeshifting Puzzles ==<br />
<br/><br />
Physical shapeshifting puzzles are hard to design, if not impossible, because of their shapeshifting nature. All the current 2D and 3D designs don't fully work, in some solved states appearing as they're scrambled.<br />
[[File:2^3_mirror_gyro.png|thumb|right|500px|2D physical 2^3 mirror before and after performing the gyro algorithm]]<br />
[[File:2D_Physical_Mirror.png|thumb|left|Drawing showing all the current 2D physical mirror cube designs(NOT fully functional)]]<br />
[[File:2^4_mirror.png|thumb|left|Render showing the current 3D physical 2^4 mirror design(NOT fully functional)]]</div>Blobinatihttp://wiki.superliminal.com/index.php?title=Canonical_Moves&diff=3492Canonical Moves2022-09-11T05:57:01Z<p>Blobinati: Created page with "If you were handed a physical 2x2x2x2 without explanation, it is not obvious how you would turn it as a puzzle. This is why the official canonical moveset exists. These are co..."</p>
<hr />
<div>If you were handed a physical 2x2x2x2 without explanation, it is not obvious how you would turn it as a puzzle. This is why the official canonical moveset exists. These are comprised of the basic moves that the community agrees on. Only these moves can be used for official solutions in the Hall of Fame. <br><br />
Watch [[https://www.youtube.com/watch?v=DzRH8BOJL8Q Melinda's video]] for a detailed overview.<br />
<br />
=History=<br />
Insert history here.<br />
<br />
=Canonical Moves=<br />
<br />
==Simple Rotation==<br />
You can 4D rotate the puzzle by rotating the cubic halves along each other symmetrically, such that the puzzle state stays the same. However, this does not allow you to reach every orientation of the puzzle. The gyro algorithm is necessary for reaching the rest of the orientation.<br />
<br />
==Cube cell turns==<br />
<br />
You can rotate the 2 cubic cells in any way you want, as this corresponds perfectly with rotating them on the physical puzzle. Melinda's video calls this an "arbitrary half puzzle juxtaposition". <br><br />
<br />
==Long cell turns==<br />
180 degree twists of the long cells, essentially like a 2x2x4 cuboid.<br />
<br />
==Gyro==<br />
<br />
<br />
<br />
<br />
<br />
=Debated Moves=<br />
Since the beginning of the canonical moveset, solvers have had to compromise which moves should be and should not be allowed. <br><br />
Most notably, Luna and others' ideas that the moves on the physical 2^4 should correspond as precisely as possible to the virtual 2^4. Things that could be included that aren't: <br><br />
<ul><br />
<li>Ux2 and Uy2</li><br />
<li>1/2 gyro move. This is a short sequence of moves that gyros one of the long faces.</li><br />
<li>More I cell reorientations using short sequences of moves</li><br />
</ul></div>Blobinatihttp://wiki.superliminal.com/index.php?title=Main_Page&diff=3491Main Page2022-09-11T05:37:08Z<p>Blobinati: </p>
<hr />
<div>==MagicCube4D==<br />
[[File:classic-hypercube.png|thumbnail|left|350px|MagicCube4D]]<br />
<br /><br />
<big>'''MagicCube 4D'''</big><br />
[http://www.superliminal.com/cube/cube.htm]<br />
<br />
For the the 4-dimensional cube puzzle accomplishments, records, and documentation, see [[MagicCube4D]].<br />
<br> <br /><br />
<big>'''Records (first and shortest)'''</big><br />
<br />
For First and Shortest check [[MC4D_Records]].<br />
<br> <br /><br />
<big>'''Gallery'''</big><br />
<br />
Check amazing pictures in [[Image_gallery]].<br />
<br><br/><br />
<big>'''Solutions'''</big><br />
<br />
Solving tips and ideas for other solutions for 4D puzzles click [[MC4D_Solutions]].<br />
<br><br/><br />
<big>'''Join this wiki community'''</big><br />
<br />
To participate in wiki editing, [[Create_Account|create an account]].<br />
<br> <br /><br />
<br> <br /><br />
<br />
==MagicTile==<br />
[[File:MagicTile.PNG|thumbnail|left|350px|MagicTile]]<br />
<br />
<br /><br />
<big>'''MagicTile V2'''</big><br />
[http://www.roice3.org/magictile/]<br />
<br /><br /><br />
<big>'''Records (first and shortest)'''</big><br />
<br /><br />
For First and Shortest check [[MagicTile_Records]].<br />
<br><br /> <br />
<big>'''List of Solvers'''</big><br />
<br /> <br />
For MagicTile v2 Solutions check [[MagicTile v2 Solutions]].<br />
<br> <br /><br />
<big>'''Mathologer Challenge'''</big><br />
<br /> <br />
See the first 100 solvers of the Klein Bottle Rubik's Analogue [[http://roice3.org/magictile/mathologer/ here]].<br />
<br> <br /><br />
<br />
<big>'''Tips and ideas</big><br />
<br /> <br />
For solving tips and ideas for MagicTile puzzles click [[MagicTile aspects]].<br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br />
==Magic Puzzle Ultimate==<br />
[[File:MPUlt_v0.3.PNG|thumbnail|left|350px|Magic Puzzle Ultimate]]<br />
<br />
<br /><br />
<big>'''Magic Puzzle Ultimate'''</big><br />
[http://cardiizastrograda.com/astr/MPUlt/]<br />
<br />
<br /><br />
<big>'''Records (first and shortest)'''</big><br />
<br />
For First and Shortest check [[MPUlt_Records]].<br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br />
==Blindfolded Solving==<br />
[[File:BLD.PNG|thumbnail|left|350px|Blindfolded solving]]<br />
<br />
<br /><br />
<big>'''Rules'''</big><br />
<br /><br />
<br />
<big>The rule of a blindfolded solution without macros:</big><br />
<br /><br />
(1) Starting the solve: make a full scramble using any simulator.<br /><br />
(2) Memorization: the solver memorizes the puzzle without making any twist. The solver may change the viewpoint to inspect the whole puzzle. The solver must not take notes (per WCA regulations). <br /><br />
(3) Put on "blindfold": Preferences > Modes > Blindfold <br /><br />
(4) During the solve: now the solver may make twists.<br /><br />
(5) Ending the solve: a successful solution ends automatically. The duration of the solution includes both the memorization phase and the solving phase.<br />
<br /><br />
<br />
<big>The rule of a blindfolded solution with macros:</big> <br />
<br /><br />
As same as the rule without macros, except: before step (1) the solver may define macros, and during step (4) the solver may use the predefined macros.<br />
<br />
<br /><br />
<br />
<big>'''Records'''</big><br />
<br /><br />
Check [[BLD_Records]].<br />
<br />
<br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br />
==Permutations==<br />
[[File:MC7Dimage.PNG|thumbnail|left|350px|MagicCube7D]]<br />
<br />
<br /><br />
<big>'''Puzzle Index'''</big><br />
<br />
Find permutation counts of every puzzle with explanations in [[Permutations_Index]].<br />
<br> <br /><br />
<big>'''Notation'''</big><br />
<br />
For a description of the notation used in the permutation count explanations, visit [[Permutations_Notation]].<br />
<br/><br />
<br> <br/><br />
<br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br />
==[[Physical Puzzle|Physical Puzzles]]==<br />
[[File:Physical3333.jpg|thumbnail|left|350px|Grant's Physical 3x3x3x3]]<br />
<br> <br/><br />
<br />
<big>'''Melinda's Physical 2x2x2x2''' </big><br />
<br> <br/><br />
In 2016, Melinda Green began making the first ever physical representation of a 4D puzzle, the 2^4. Check out her page [https://superliminal.com/cube/2x2x2x2/ here].<br />
<br><br/><br />
For different solving methods, visit [[Physical 2^4 Methods]]. <br><br />
For speedsolving records, visit [[Physical 2^4 Records]], but make sure to be familiar with the [[Canonical Moves]] first.<br />
<br />
<br> <br/><br />
<br />
<big>'''Grant's Puzzles''' </big><br />
<br><br/><br />
Grant designed and 3D printed his own puzzles based on Melinda's 2x2x2x2 piece design. He made a 2x2x2x3, 2x2x3x3, 3x3x3x2, and the holy grail, the 3x3x3x3.<br />
For more information on Grant's puzzles, visit [[Grant's Physical 4d Puzzles]]</div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_2%5E4_Records&diff=3459Physical 2^4 Records2022-08-16T03:36:36Z<p>Blobinati: </p>
<hr />
<div>This page contains the unofficial records for timed speed solves of Melinda's Physical 2x2x2x2. Add your accomplishments to the tables below, following the existing patterns. You are honor bound to be accurate in your claims. Please add a link to your solve video. <br><br />
<br />
"Official" Regulations: <br><br />
<ul><br />
<li>You must use the official [[https://www.youtube.com/watch?v=DzRH8BOJL8Q canonical moveset]]. (Which is currently kind of disputed, but maybe we'll figure it out one day lol)</li><br />
<li>You are allowed to gyro and do 4D rotations during inspection</li><br />
<li>If piece(s) fall out accidentally, you may replace them, not worrying about if you put them back the wrong way or not. Then you are allowed to fix any weird errors due to that during the solve</li><br />
<li>If you do an illegal move, you may NOT fix it later, and that is a DNF</li><br />
</ul><br />
<br />
<br />
<br /><br />
<center><br />
{|border="1" cellpadding="5"<br />
|-<br />
!colspan="9"|<big>Official Records</big><br />
|-<br />
!colspan="3"|Two Handed<br />
!colspan="3"|One Handed<br />
!colspan="3"|BLD<br />
|-<br />
!Date||Name||Time||Date||Name||Time||Date||Name||Time<br />
|-<br />
|2019/8/11||Connor Lindsay||[[https://www.youtube.com/watch?v=oEdrWPEsKPQ 2:26]]<br />
|2022/07/31||Rowan Fortier||[[https://www.youtube.com/watch?v=ClqLrac3Ib4 6:25.12]] <br />
|2022/08/08||Asa Kaplan||[[https://www.youtube.com/watch?v=lBssOimXaFE 47:14]]<br />
|-<br />
|2021/11/15||Rowan Fortier||[[https://youtu.be/mgfhSL2fi7E 2:16.538]]<br />
|-<br />
|2021/12/6||Rowan Fortier||[[https://youtu.be/tOaBQs34oB0 2:05.27]]<br />
|-<br />
|2021/12/9||Rowan Fortier||[[https://youtu.be/I9hnsif4ImE 2:03.582]]<br />
|-<br />
|2021/12/11||Rowan Fortier||[[https://youtu.be/2SWo0zMlg8I 2:00.656]]<br />
|-<br />
|2021/12/11||Rowan Fortier||[[https://youtu.be/JJPJ7hgNLJU 1:56.748]]<br />
|-<br />
|2022/05/07||Rowan Fortier||[[https://youtu.be/RuUc26S5xpw 1:46.24]]<br />
|-<br />
|2022/06/20||Rowan Fortier||[[https://youtu.be/FSpuv9FJorw 1:28.14]]<br />
|-<br />
|2022/08/02||Rowan Fortier||[[https://youtu.be/XDW7wi4ryPE 1:27.17]]<br />
|-<br />
|2022/08/07||Grant S||[[https://www.youtube.com/watch?v=uEnk2yrJN7I 1:23.28]]<br />
|-<br />
|2022/08/12||Grant S||[[https://www.youtube.com/watch?v=X_FY-CUfvUI 1:07.57]]<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<center><br />
{|border="1" cellpadding="5"<br />
|-<br />
!colspan="5"|<big>Unnofficial Records</big><br />
|-<br />
!Date||Name||Time||Type||Comments<br />
|-<br />
| ||Rowan Fortier||1:11.17||Speed||PB but not WR<br />
|-<br />
|2022/08/15||William Jestin Palmer||2:12.69||Speed||New Zealand Record<br />
|}</div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_2%5E4_Records&diff=3458Physical 2^4 Records2022-08-15T04:06:25Z<p>Blobinati: </p>
<hr />
<div>This page contains the unofficial records for timed speed solves of Melinda's Physical 2x2x2x2. Add your accomplishments to the tables below, following the existing patterns. You are honor bound to be accurate in your claims. Please add a link to your solve video.<br />
<br />
<br />
<br /><br />
<center><br />
{|border="1" cellpadding="5"<br />
|-<br />
!colspan="9"|<big>Official Records</big><br />
|-<br />
!colspan="3"|Two Handed<br />
!colspan="3"|One Handed<br />
!colspan="3"|BLD<br />
|-<br />
!Date||Name||Time||Date||Name||Time||Date||Name||Time<br />
|-<br />
|2019/8/11||Connor Lindsay||[[https://www.youtube.com/watch?v=oEdrWPEsKPQ 2:26]]<br />
|2022/07/31||Rowan Fortier||[[https://www.youtube.com/watch?v=ClqLrac3Ib4 6:25.12]] <br />
|2022/08/08||Asa Kaplan||[[https://www.youtube.com/watch?v=lBssOimXaFE 47:14]]<br />
|-<br />
|2021/11/15||Rowan Fortier||[[https://youtu.be/mgfhSL2fi7E 2:16.538]]<br />
|-<br />
|2021/12/6||Rowan Fortier||[[https://youtu.be/tOaBQs34oB0 2:05.27]]<br />
|-<br />
|2021/12/9||Rowan Fortier||[[https://youtu.be/I9hnsif4ImE 2:03.582]]<br />
|-<br />
|2021/12/11||Rowan Fortier||[[https://youtu.be/2SWo0zMlg8I 2:00.656]]<br />
|-<br />
|2021/12/11||Rowan Fortier||[[https://youtu.be/JJPJ7hgNLJU 1:56.748]]<br />
|-<br />
|2022/05/07||Rowan Fortier||[[https://youtu.be/RuUc26S5xpw 1:46.24]]<br />
|-<br />
|2022/06/20||Rowan Fortier||[[https://youtu.be/FSpuv9FJorw 1:28.14]]<br />
|-<br />
|2022/08/02||Rowan Fortier||[[https://youtu.be/XDW7wi4ryPE 1:27.17]]<br />
|-<br />
|2022/08/07||Grant S||[[https://www.youtube.com/watch?v=uEnk2yrJN7I 1:23.28]]<br />
|-<br />
|2022/08/12||Grant S||[[https://www.youtube.com/watch?v=X_FY-CUfvUI 1:07.57]]<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<center><br />
{|border="1" cellpadding="5"<br />
|-<br />
!colspan="5"|<big>Unnofficial Records</big><br />
|-<br />
!Date||Name||Time||Type||Comments<br />
|-<br />
| ||Rowan Fortier||1:11.17||Speed||PB but not WR<br />
|-<br />
|2022-08-15||William Jestin Palmer||2:12.69||Speed||New Zealand Record<br />
|}</div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_2%5E4_Methods&diff=3457Physical 2^4 Methods2022-08-15T04:05:32Z<p>Blobinati: </p>
<hr />
<div>Thanks to William Jestin Palmer (Hyperespy) for the diagram template!<br />
=Notation=<br />
<br />
Because this is a physical puzzle, we can easily adapt x, y, & z rotations to fit the moves. The puzzle is held horizontally throughout most of the solve, so the L and R cells can do any x, y, & z rotations freely. The I and O cells can do any x rotation, as well as only y2 or z2 rotations. The other sides have restricted turning due to the projection, and can only do 180 degree twists, so they will just be referred to as U2, D2, F2, B2.<br />
<br />
=Gyro Algorithm=<br />
[[File:GyroGif.gif|thumbnail|left|300px|Gyro algorithm]]<br />
From a solved puzzle, there's nothing you can do to change the orbits of the L/R stickers, so we need an algorithm to do a special 4D rotation of the puzzle, called a gyro. <br><br />
A commonly used algorithm for the Gyro is: <br><br />
<ul><br />
<li>Take the left endcap off and put it on the right so it becomes the right endcap (this brings the puzzle into the inverted state)</li><br />
<li>Ly Ry'</li><br />
<li>Take the right endcap off and put it on the left so it becomes the left endcap (this brings the puzzle back into the normal state)</li><br />
<li> Rx2 B2 D2 Lx2</li><br />
</ul><br />
Note that the last 2 moves (D2 Lx2) could be replaced by D2 Rx2, U2 Lx2, or U2 Rx2 based on the solver's preference. <br><br />
Watch [[https://www.youtube.com/watch?v=Et9JuxPFl2g Melinda's 6 Snap Gyro]] for an alternative algorithm. <br><br />
<br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br />
=Orienting Both Cells=<br />
==Grant's Method==<br />
[[File:Grant8UD.png|thumbnail|left|Exactly 8 oriented to the U/D axis]]<br />
[[File:Grant8L8R.png|thumbnail|left|8 on L, 8 on the U/D axis of R]]<br />
<ul><br />
<li>The first step is to get EXACTLY 8 pieces from an opposite colour group oriented to U/D. They can be in any position, as shown in the diagram, but must be oriented to the U/D axis. Make sure that there are exactly 8, then perform the gyro algorithm</li><br />
<li>Use inspection time to count which of the 4 sets of colours have the most oriented to U/D, and start with that set.</li><br />
<li>Pair up the other 8 pieces into a cell where they are oriented to U/D. This will end up separating the pieces that you oriented in the first step onto it's own cell</li><br />
<li>Rotate the R cell so the pieces are oriented to the I/O axis (a z or z' rotation). Then perform the gyro algorithm</li> <br />
<li>Undo the last 2 moves of the gyro. Then just undo that Rz or Rz', and do another gyro</li><br />
<li>Now you will have all 16 corners oriented to the L/R axis</li><br />
</ul><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br />
==Rowan's Method==<br />
[[File:Rowan4orLess.png|thumbnail|left|4 or less corners oriented to L/R]] [[File:Rowan12UD.png|thumbnail|left|12 oriented to U/D]] <br><br />
<ul><br />
<li>To start, you want to pick an axis that has 4 or fewer corners oriented to L/R (4 does happen to be the easiest case, but fewer than 4 is fine)</li> <li>Use block building or RKT to orient a cell's U/D axis</li><br />
<li>Use RKT to build a layer on the opposite cell, orienting 12 corners to U/D</li><br />
<li>Do the gyro algorithm to get the 12 corners to the L/R axis</li><br />
<li>Setup the 4 (or fewer) corners into one of these OCLL cases (H, Sune/Antisune, U) depending on how many corners you counted at the beginning</li><br />
<li>Gyro again, then solve the OCLL case using RKT. (<big>Hint:</big> you can use the [[https://www.speedsolving.com/wiki/index.php/OLL_(2x2x2) Guimond algorithms]] (marked with a G) to save a few moves)</li><br />
<li>Once all 16 corners are oriented to U/D, use the gyro algorithm to get them all oriented to L/R</li><br />
</ul><br />
<br />
<br><br />
<br><br />
<br><br />
<br><br />
<br />
=Permuting Both Cells=<br />
==P4L==<br />
Originally developed by Connor Lindsay as PAL (Permuting All Layers), P4L permutes all 4 layers at the same time once they are separated - an exact dimensional analogy of the 2^3 Ortega method.<br />
<ul><br />
<li>Block build a cell whose layers are oriented, but not necessarily permuted correctly</li><br />
<li>Use RKT to orient 2 opposite layers of the last cell, just like in the Ortega 2^3 method</li><br />
<li>Execute an algorithm to permute all 4 layers at once<li><br />
</ul> <br><br />
You can also learn only a handful of algorithms, and learn advanced case manipulation to morph a bad case into a good one. Some cases are the same as 2^3 algs, and other are like domino cube 2^3 algs. <br><br />
==CBC==<br />
<ul><br />
<li>Directly solve one of the cells using block building or RKT techniques </li><br />
<li>Solve the last cell using RKT</li> <br><br />
=RKT Parity=<br />
If you end the solve and a single layer needs twisting by 180 degrees, then do this algorithm with RKT: <br><br />
<ul><br />
<li>R2 B2 R2 U R2 B2 R2 U</li><br />
</ul><br />
There is also [[https://www.youtube.com/watch?v=kX6usOCsAd4 this]] video by Melinda with many alternative algorithms.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_2%5E4_Records&diff=3456Physical 2^4 Records2022-08-15T03:59:54Z<p>Blobinati: </p>
<hr />
<div>This page contains the unofficial records for timed speed solves of Melinda's Physical 2x2x2x2. Add your accomplishments to the tables below, following the existing patterns. You are honor bound to be accurate in your claims. Please add a link to your solve video.<br />
<br />
<br />
<br /><br />
<center><br />
{|border="1" cellpadding="5"<br />
|-<br />
!colspan="9"|<big>Official Records</big><br />
|-<br />
!colspan="3"|Two Handed<br />
!colspan="3"|One Handed<br />
!colspan="3"|BLD<br />
|-<br />
!Date||Name||Time||Date||Name||Time||Date||Name||Time<br />
|-<br />
|2019/8/11||Connor Lindsay||[[https://www.youtube.com/watch?v=oEdrWPEsKPQ 2:26]]<br />
|2022/07/31||Rowan Fortier||[[https://www.youtube.com/watch?v=ClqLrac3Ib4 6:25.12]] <br />
|2022/08/08||Asa Kaplan||[[https://www.youtube.com/watch?v=lBssOimXaFE 47:14]]<br />
|-<br />
|2021/11/15||Rowan Fortier||[[https://youtu.be/mgfhSL2fi7E 2:16.538]]<br />
|-<br />
|2021/12/6||Rowan Fortier||[[https://youtu.be/tOaBQs34oB0 2:05.27]]<br />
|-<br />
|2021/12/9||Rowan Fortier||[[https://youtu.be/I9hnsif4ImE 2:03.582]]<br />
|-<br />
|2021/12/11||Rowan Fortier||[[https://youtu.be/2SWo0zMlg8I 2:00.656]]<br />
|-<br />
|2021/12/11||Rowan Fortier||[[https://youtu.be/JJPJ7hgNLJU 1:56.748]]<br />
|-<br />
|2022/05/07||Rowan Fortier||[[https://youtu.be/RuUc26S5xpw 1:46.24]]<br />
|-<br />
|2022/06/20||Rowan Fortier||[[https://youtu.be/FSpuv9FJorw 1:28.14]]<br />
|-<br />
|2022/08/02||Rowan Fortier||[[https://youtu.be/XDW7wi4ryPE 1:27.17]]<br />
|-<br />
|2022/08/07||Grant S||[[https://www.youtube.com/watch?v=uEnk2yrJN7I 1:23.28]]<br />
|-<br />
|2022/08/12||Grant S||[[https://www.youtube.com/watch?v=X_FY-CUfvUI 1:07.57]]<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<center><br />
{|border="1" cellpadding="5"<br />
|-<br />
!colspan="5"|<big>Unnofficial Records</big><br />
|-<br />
!Date||Name||Time||Type||Comments<br />
|-<br />
| ||Rowan Fortier||1:11.17||Speed||PB but not WR<br />
|-<br />
|2022-08-15||William Palmer||2:12.69||Speed||<br />
|}</div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_2%5E4_Methods&diff=3455Physical 2^4 Methods2022-08-13T21:27:11Z<p>Blobinati: </p>
<hr />
<div>=Notation=<br />
<br />
Because this is a physical puzzle, we can easily adapt x, y, & z rotations to fit the moves. The puzzle is held horizontally throughout most of the solve, so the L and R cells can do any x, y, & z rotations freely. The I and O cells can do any x rotation, as well as only y2 or z2 rotations. The other sides have restricted turning due to the projection, and can only do 180 degree twists, so they will just be referred to as U2, D2, F2, B2.<br />
<br />
=Gyro Algorithm=<br />
[[File:GyroGif.gif|thumbnail|left|300px|Gyro algorithm]]<br />
From a solved puzzle, there's nothing you can do to change the orbits of the L/R stickers, so we need an algorithm to do a special 4D rotation of the puzzle, called a gyro. <br><br />
A commonly used algorithm for the Gyro is: <br><br />
<ul><br />
<li>Take the left endcap off and put it on the right so it becomes the right endcap (this brings the puzzle into the inverted state)</li><br />
<li>Ly Ry'</li><br />
<li>Take the right endcap off and put it on the left so it becomes the left endcap (this brings the puzzle back into the normal state)</li><br />
<li> Rx2 B2 D2 Lx2</li><br />
</ul><br />
Note that the last 2 moves (D2 Lx2) could be replaced by D2 Rx2, U2 Lx2, or U2 Rx2 based on the solver's preference. <br><br />
Watch [[https://www.youtube.com/watch?v=Et9JuxPFl2g Melinda's 6 Snap Gyro]] for an alternative algorithm. <br><br />
<br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br />
=Orienting Both Cells=<br />
==Grant's Method==<br />
[[File:Grant8UD.png|thumbnail|left|Exactly 8 oriented to the U/D axis]]<br />
[[File:Grant8L8R.png|thumbnail|left|8 on L, 8 on the U/D axis of R]]<br />
<ul><br />
<li>The first step is to get EXACTLY 8 pieces from an opposite colour group oriented to U/D. They can be in any position, as shown in the diagram, but must be oriented to the U/D axis. Make sure that there are exactly 8, then perform the gyro algorithm</li><br />
<li>Use inspection time to count which of the 4 sets of colours have the most oriented to U/D, and start with that set.</li><br />
<li>Pair up the other 8 pieces into a cell where they are oriented to U/D. This will end up separating the pieces that you oriented in the first step onto it's own cell</li><br />
<li>Rotate the R cell so the pieces are oriented to the I/O axis (a z or z' rotation). Then perform the gyro algorithm</li> <br />
<li>Undo the last 2 moves of the gyro. Then just undo that Rz or Rz', and do another gyro</li><br />
<li>Now you will have all 16 corners oriented to the L/R axis</li><br />
</ul><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br />
==Rowan's Method==<br />
[[File:Rowan4orLess.png|thumbnail|left|4 or less corners oriented to L/R]] [[File:Rowan12UD.png|thumbnail|left|12 oriented to U/D]] <br><br />
<ul><br />
<li>To start, you want to pick an axis that has 4 or fewer corners oriented to L/R (4 does happen to be the easiest case, but fewer than 4 is fine)</li> <li>Use block building or RKT to orient a cell's U/D axis</li><br />
<li>Use RKT to build a layer on the opposite cell, orienting 12 corners to U/D</li><br />
<li>Do the gyro algorithm to get the 12 corners to the L/R axis</li><br />
<li>Setup the 4 (or fewer) corners into one of these OCLL cases (H, Sune/Antisune, U) depending on how many corners you counted at the beginning</li><br />
<li>Gyro again, then solve the OCLL case using RKT. (<big>Hint:</big> you can use the [[https://www.speedsolving.com/wiki/index.php/OLL_(2x2x2) Guimond algorithms]] (marked with a G) to save a few moves)</li><br />
<li>Once all 16 corners are oriented to U/D, use the gyro algorithm to get them all oriented to L/R</li><br />
</ul><br />
<br />
<br><br />
<br><br />
<br><br />
<br><br />
<br />
=Permuting Both Cells=<br />
==P4L==<br />
Originally developed by Connor Lindsay as PAL (Permuting All Layers), P4L permutes all 4 layers at the same time once they are separated - an exact dimensional analogy of the 2^3 Ortega method.<br />
<ul><br />
<li>Block build a cell whose layers are oriented, but not necessarily permuted correctly</li><br />
<li>Use RKT to orient 2 opposite layers of the last cell, just like in the Ortega 2^3 method</li><br />
<li>Execute an algorithm to permute all 4 layers at once<li><br />
</ul> <br><br />
You can also learn only a handful of algorithms, and learn advanced case manipulation to morph a bad case into a good one. Some cases are the same as 2^3 algs, and other are like domino cube 2^3 algs. <br><br />
==CBC==<br />
<ul><br />
<li>Directly solve one of the cells using block building or RKT techniques </li><br />
<li>Solve the last cell using RKT</li> <br><br />
=RKT Parity=<br />
If you end the solve and a single layer needs twisting by 180 degrees, then do this algorithm with RKT: <br><br />
<ul><br />
<li>R2 B2 R2 U R2 B2 R2 U</li><br />
</ul><br />
There is also [[https://www.youtube.com/watch?v=kX6usOCsAd4 this]] video by Melinda with many alternative algorithms.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_2%5E4_Methods&diff=3454Physical 2^4 Methods2022-08-13T21:13:23Z<p>Blobinati: </p>
<hr />
<div>=Notation=<br />
<br />
Because this is a physical puzzle, we can easily adapt x, y, & z rotations to fit the moves. The puzzle is held horizontally throughout most of the solve, so the L and R cells can do any x, y, & z rotations freely. The I and O cells can do any x rotation, as well as only y2 or z2 rotations. The other sides have restricted turning due to the projection, and can only do 180 degree twists, so they will just be referred to as U2, D2, F2, B2.<br />
<br />
=Gyro Algorithm=<br />
[[File:GyroGif.gif|thumbnail|left|300px|Gyro algorithm]]<br />
From a solved puzzle, there's nothing you can do to change the orbits of the L/R stickers, so we need an algorithm to do a special 4D rotation of the puzzle, called a gyro. <br><br />
A commonly used algorithm for the Gyro is: <br><br />
<ul><br />
<li>Take the left endcap off and put it on the right so it becomes the right endcap (this brings the puzzle into the inverted state)</li><br />
<li>Ly Ry'</li><br />
<li>Take the right endcap off and put it on the left so it becomes the left endcap (this brings the puzzle back into the normal state)</li><br />
<li> Rx2 B2 D2 Lx2</li><br />
</ul><br />
Note that the last 2 moves (D2 Lx2) could be replaced by D2 Rx2, U2 Lx2, or U2 Rx2 based on the solver's preference. <br><br />
Watch [[https://www.youtube.com/watch?v=Et9JuxPFl2g Melinda's 6 Snap Gyro]] for an alternative algorithm. <br><br />
<br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br />
=Orienting Both Cells=<br />
==Grant's Method==<br />
[[File:Grant8UD.png|thumbnail|left|Exactly 8 oriented to the U/D axis]]<br />
[[File:Grant8L8R.png|thumbnail|left|8 on L, 8 on the U/D axis of R]]<br />
<ul><br />
<li>The first step is to get EXACTLY 8 pieces from an opposite colour group oriented to U/D. They can be in any position, as shown in the diagram, but must be oriented to the U/D axis. Make sure that there are exactly 8, then perform the gyro algorithm</li><br />
<li>Use inspection time to count which of the 4 sets of colours have the most oriented to U/D, and start with that set.</li><br />
<li>Pair up the other 8 pieces into a cell where they are oriented to U/D. This will end up separating the pieces that you oriented in the first step onto it's own cell</li><br />
<li>Rotate the R cell so the pieces are oriented to the I/O axis (a z or z' rotation). Then perform the gyro algorithm</li> <br />
<li>Undo the last 2 moves of the gyro. Then just undo that Rz or Rz', and do another gyro</li><br />
<li>Now you will have all 16 corners oriented to the L/R axis</li><br />
</ul><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br />
==Rowan's Method==<br />
[[File:Rowan4orLess.png|thumbnail|left|4 or less corners oriented to L/R]] [[File:Rowan12UD.png|thumbnail|left|12 oriented to U/D]] <br><br />
<ul><br />
<li>To start, you want to pick an axis that has 4 or fewer corners oriented to L/R (4 does happen to be the easiest case, but fewer than 4 is fine)</li> <li>Use block building or RKT to orient a cell's U/D axis</li><br />
<li>Use RKT to build a layer on the opposite cell, orienting 12 corners to U/D</li><br />
<li>Do the gyro algorithm to get the 12 corners to the L/R axis</li><br />
<li>Setup the 4 (or fewer) corners into one of these OCLL cases (H, Sune/Antisune, U) depending on how many corners you counted at the beginning</li><br />
<li>Gyro again, then solve the OCLL case using RKT. (<big>Hint:</big> you can use the [[https://www.speedsolving.com/wiki/index.php/OLL_(2x2x2) Guimond algorithms]] (marked with a G) to save a few moves)</li><br />
<li>Once all 16 corners are oriented to U/D, use the gyro algorithm to get them all oriented to L/R</li><br />
</ul><br />
<br />
<br />
<br />
=Permuting Both Cells=<br />
==P4L==<br />
==CBC==<br />
Directly solve one of the cells, then use RKT to solve the other cell<br />
=RKT Parity=<br />
If you end the solve and a single layer needs twisting by 180 degrees, then do this algorithm with RKT: <br><br />
<ul><br />
<li>R2 B2 R2 U R2 B2 R2 U</li><br />
</ul><br />
There is also [[https://www.youtube.com/watch?v=kX6usOCsAd4 this]] video by Melinda with many alternative algorithms.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=File:RowanHcase.png&diff=3453File:RowanHcase.png2022-08-13T20:50:54Z<p>Blobinati: </p>
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<div></div>Blobinatihttp://wiki.superliminal.com/index.php?title=File:Rowan12UD.png&diff=3452File:Rowan12UD.png2022-08-13T20:50:43Z<p>Blobinati: </p>
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<div></div>Blobinatihttp://wiki.superliminal.com/index.php?title=File:Rowan8UD.png&diff=3451File:Rowan8UD.png2022-08-13T20:49:58Z<p>Blobinati: </p>
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<div></div>Blobinatihttp://wiki.superliminal.com/index.php?title=File:Rowan4orLess.png&diff=3450File:Rowan4orLess.png2022-08-13T20:49:33Z<p>Blobinati: </p>
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<div></div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_2%5E4_Methods&diff=3449Physical 2^4 Methods2022-08-13T18:50:26Z<p>Blobinati: </p>
<hr />
<div>=Notation=<br />
<br />
Because this is a physical puzzle, we can easily adapt x, y, & z rotations to fit the moves. The puzzle is held horizontally throughout most of the solve, so the L and R cells can do any x, y, & z rotations freely. The I and O cells can do any x rotation, as well as only y2 or z2 rotations. The other sides have restricted turning due to the projection, and can only do 180 degree twists, so they will just be referred to as U2, D2, F2, B2.<br />
<br />
=Gyro Algorithm=<br />
[[File:GyroGif.gif|thumbnail|left|300px|Gyro algorithm]]<br />
From a solved puzzle, there's nothing you can do to change the orbits of the L/R stickers, so we need an algorithm to do a special 4D rotation of the puzzle, called a gyro. <br><br />
A commonly used algorithm for the Gyro is: <br><br />
<ul><br />
<li>Take the left endcap off and put it on the right so it becomes the right endcap (this brings the puzzle into the inverted state)</li><br />
<li>Ly Ry'</li><br />
<li>Take the right endcap off and put it on the left so it becomes the left endcap (this brings the puzzle back into the normal state)</li><br />
<li> Rx2 B2 D2 Lx2</li><br />
</ul><br />
Note that the last 2 moves (D2 Lx2) could be replaced by D2 Rx2, U2 Lx2, or U2 Rx2 based on the solver's preference. <br><br />
Watch [[https://www.youtube.com/watch?v=Et9JuxPFl2g Melinda's 6 Snap Gyro]] for an alternative algorithm. <br><br />
<br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br />
=Orienting Both Cells=<br />
==Grant's Method==<br />
[[File:Grant8UD.png|thumbnail|left|Exactly 8 oriented to the U/D axis]]<br />
The first step is to get EXACTLY 8 pieces from an opposite colour group oriented to U/D. They can be in any position, as shown in the diagram, but must be oriented to the U/D axis. Make sure that there are exactly 8, then perform the gyro algorithm. <br><br />
Tips: <br><br />
<ul><br />
<li>Use inspection time to count which of the 4 sets of colours has the most oriented to U/D, and start with that set.</li><br />
<li>This should only take a few moves, and is very intuitive.</li><br />
</ul><br />
<br><br />
[[File:Grant8L8R.png|thumbnail|left|8 on L, 8 on the U/D axis of R]]<br />
<br><br />
Next, pair up the other 8 pieces into a cell where they are oriented to U/D. This will end up separating the pieces that you oriented in the last step onto it's own cell. <br><br />
From this position, you want to rotate the R cell so the pieces are oriented to the I/O axis (a z or z' rotation). Then perform the gyro algorithm, but undo the last 2 moves of the gyro. Then just undo that Rz or Rz', and do another gyro. <br><br />
Now you will have all 16 corners oriented to the L/R axis. <br><br />
<br />
==Rowan's Method==<br />
<br />
=Permuting Both Cells=<br />
==P4L==<br />
==CBC==<br />
Directly solve one of the cells, then use RKT to solve the other cell<br />
=RKT Parity=<br />
If you end the solve and a single layer needs twisting by 180 degrees, then do this algorithm with RKT: <br><br />
<ul><br />
<li>R2 B2 R2 U R2 B2 R2 U</li><br />
</ul><br />
There is also [[https://www.youtube.com/watch?v=kX6usOCsAd4 this]] video by Melinda with many alternative algorithms.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=File:Grant8L8R.png&diff=3448File:Grant8L8R.png2022-08-13T18:26:00Z<p>Blobinati: </p>
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<div></div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_2%5E4_Methods&diff=3447Physical 2^4 Methods2022-08-13T18:20:02Z<p>Blobinati: </p>
<hr />
<div>=Notation=<br />
<br />
Because this is a physical puzzle, we can easily adapt x, y, & z rotations to fit the moves. The puzzle is held horizontally throughout most of the solve, so the L and R cells can do any x, y, & z rotations freely. The I and O cells can do any x rotation, as well as only y2 or z2 rotations. The other sides have restricted turning due to the projection, and can only do 180 degree twists, so they will just be referred to as U2, D2, F2, B2.<br />
<br />
=Gyro Algorithm=<br />
[[File:GyroGif.gif|thumbnail|left|300px|Gyro algorithm]]<br />
From a solved puzzle, there's nothing you can do to change the orbits of the L/R stickers, so we need an algorithm to do a special 4D rotation of the puzzle, called a gyro. <br><br />
A commonly used algorithm for the Gyro is: <br><br />
<ul><br />
<li>Take the left endcap off and put it on the right so it becomes the right endcap (this brings the puzzle into the inverted state)</li><br />
<li>Ly Ry'</li><br />
<li>Take the right endcap off and put it on the left so it becomes the left endcap (this brings the puzzle back into the normal state)</li><br />
<li> Rx2 B2 D2 Lx2</li><br />
</ul><br />
Note that the last 2 moves (D2 Lx2) could be replaced by D2 Rx2, U2 Lx2, or U2 Rx2 based on the solver's preference. <br><br />
Watch [[https://www.youtube.com/watch?v=Et9JuxPFl2g Melinda's 6 Snap Gyro]] for an alternative algorithm. <br><br />
<br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br><br />
<br />
=Orienting Both Cells=<br />
==Grant's Method==<br />
This method uses <big>NO</big> algorithms!<br />
===Orient 8/16===<br />
[[File:Grant8UD.png|thumbnail|left|Exactly 8 oriented to the U/D axis]]<br />
The first step is to get EXACTLY 8 pieces from an opposite colour group oriented to U/D. They can be in any position, as shown in the diagram, but must be oriented to the U/D axis. Make sure that there are exactly 8, then perform the gyro algorithm. <br><br />
Tips: <br><br />
<ul><br />
<li>Use inspection time to count which of the 4 sets of colours has the most oriented to U/D, and start with that set.</li><br />
<li>This should only take a few moves, and is very intuitive.</li><br />
</ul><br />
<br><br />
===Orient 16/16===<br />
<br />
==Rowan's Method==<br />
<br />
=Permuting Both Cells=<br />
==P4L==<br />
==CBC==<br />
Directly solve one of the cells, then use RKT to solve the other cell<br />
=RKT Parity=<br />
If you end the solve and a single layer needs twisting by 180 degrees, then do this algorithm with RKT: <br><br />
<ul><br />
<li>R2 B2 R2 U R2 B2 R2 U</li><br />
</ul><br />
There is also [[https://www.youtube.com/watch?v=kX6usOCsAd4 this]] video by Melinda with many alternative algorithms.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=File:Grant8UD.png&diff=3446File:Grant8UD.png2022-08-13T18:06:41Z<p>Blobinati: </p>
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<div></div>Blobinatihttp://wiki.superliminal.com/index.php?title=File:PhysVirtAnimation.gif&diff=3445File:PhysVirtAnimation.gif2022-08-13T17:52:07Z<p>Blobinati: </p>
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<div></div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_2%5E4_Methods&diff=3444Physical 2^4 Methods2022-08-13T17:46:45Z<p>Blobinati: </p>
<hr />
<div>=Notation=<br />
<br />
Because this is a physical puzzle, we can easily adapt x, y, & z rotations to fit the moves. The puzzle is held horizontally throughout most of the solve, so the L and R cells can do any x, y, & z rotations freely. The I and O cells can do any x rotation, as well as only y2 or z2 rotations. The other sides have restricted turning due to the projection, and can only do 180 degree twists, so they will just be referred to as U2, D2, F2, B2.<br />
<br />
=Gyro Algorithm=<br />
[[File:GyroGif.gif|thumbnail|left|300px|Gyro algorithm]]<br />
From a solved puzzle, there's nothing you can do to change the orbits of the L/R stickers, so we need an algorithm to do a special 4D rotation of the puzzle, called a gyro. <br><br />
A commonly used algorithm for the Gyro is: <br><br />
<ul><br />
<li>Take the left endcap off and put it on the right so it becomes the right endcap (this brings the puzzle into the inverted state)</li><br />
<li>Ly Ry'</li><br />
<li>Take the right endcap off and put it on the left so it becomes the left endcap (this brings the puzzle back into the normal state)</li><br />
<li> Rx2 B2 D2 Lx2</li><br />
</ul><br />
Note that the last 2 moves (D2 Lx2) could be replaced by D2 Rx2, U2 Lx2, or U2 Rx2 based on the solver's preference. <br><br />
Watch [[https://www.youtube.com/watch?v=Et9JuxPFl2g Melinda's 6 Snap Gyro]] for an alternative algorithm. <br><br />
<br />
<br><br />
<br><br />
<br><br />
<br />
=Orienting Both Cells=<br />
==Grant's Method==<br />
This method uses <big>NO</big> algorithms! The first step is to get exactly 8 pieces from a opposite colour group oriented to U/D. Then you do a gyro algorithm, which brings those 8 to the L/R stickers. Because you oriented exactly 8, that means that the other 8 are all in good positions to be paired up onto a single cell oriented to U/D. Next, rotate the side that has 8 oriented to U/D like a z or z' such that they are oriented to I/O. Do a gyro algorithm, then undo the last 3 moves of the gyro, and then gyro again.<br />
<br />
==Rowan's Method==<br />
<br />
=Permuting Both Cells=<br />
==P4L==<br />
==CBC==<br />
Directly solve one of the cells, then use RKT to solve the other cell<br />
=RKT Parity=<br />
If you end the solve and a single layer needs twisting by 180 degrees, then do this algorithm with RKT: <br><br />
<ul><br />
<li>R2 B2 R2 U R2 B2 R2 U</li><br />
</ul><br />
There is also [[https://www.youtube.com/watch?v=kX6usOCsAd4 this]] video by Melinda with many alternative algorithms.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=File:GyroGif.gif&diff=3443File:GyroGif.gif2022-08-13T17:37:54Z<p>Blobinati: </p>
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<div></div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_2%5E4_Methods&diff=3442Physical 2^4 Methods2022-08-13T17:25:21Z<p>Blobinati: Created page with "=Notation= Because this is a physical puzzle, we can easily adapt x, y, & z rotations to fit the moves. The puzzle is held horizontally throughout most of the solve, so the L..."</p>
<hr />
<div>=Notation=<br />
<br />
Because this is a physical puzzle, we can easily adapt x, y, & z rotations to fit the moves. The puzzle is held horizontally throughout most of the solve, so the L and R cells can do any x, y, & z rotations freely. The I and O cells can do any x rotation, as well as only y2 or z2 rotations. The other sides have restricted turning due to the projection, and can only do 180 degree twists, so they will just be referred to as U2, D2, F2, B2.<br />
<br />
=Gyro Algorithm=<br />
<br />
From a solved puzzle, there's nothing you can do to change the orbits of the L/R stickers, so we need an algorithm to do a special 4D rotation of the puzzle, called a gyro. <br><br />
A commonly used algorithm for the Gyro is: <br><br />
<ul><br />
<li>Take the left endcap off and put it on the right so it becomes the right endcap (this brings the puzzle into the inverted state)</li><br />
<li>Ly Ry'</li><br />
<li>Take the right endcap off and put it on the left so it becomes the left endcap (this brings the puzzle back into the normal state)</li><br />
<li> Rx2 B2 D2 Lx2</li><br />
</ul><br />
Note that the last 2 moves (D2 Lx2) could be replaced by D2 Rx2, U2 Lx2, or U2 Rx2 based on the solver's preference.<br />
<br />
=Orienting Both Cells=<br />
==Grant's Method==<br />
This method uses <big>NO</big> algorithms! The first step is to get exactly 8 pieces from a opposite colour group oriented to U/D. Then you do a gyro algorithm, which brings those 8 to the L/R stickers. Because you oriented exactly 8, that means that the other 8 are all in good positions to be paired up onto a single cell oriented to U/D. Next, rotate the side that has 8 oriented to U/D like a z or z' such that they are oriented to I/O. Do a gyro algorithm, then undo the last 3 moves of the gyro, and then gyro again.<br />
<br />
==Rowan's Method==<br />
<br />
=Permuting Both Cells=<br />
==P4L==<br />
==CBC==<br />
Directly solve one of the cells, then use RKT to solve the other cell<br />
=RKT Parity=<br />
If you end the solve and a single layer needs twisting by 180 degrees, then do this algorithm with RKT: <br><br />
<ul><br />
<li>R2 B2 R2 U R2 B2 R2 U</li><br />
</ul><br />
There is also [[https://www.youtube.com/watch?v=kX6usOCsAd4 this]] video by Melinda with many alternative algorithms.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=3%5E4&diff=34413^42022-08-13T16:50:49Z<p>Blobinati: </p>
<hr />
<div>Visit [[Notation]] to get an overview of the different notation systems to describe moves on the 3^4. <br><br />
<br />
==RKT==<br />
RKT is a technique that is used to execute moves that damage fewer pieces. By using RKT, the solver picks a cell that the solver wants to treat i.e. as a 3^3 (If it was a 4^4 you were solving, RKT would treat a cell as a 4^3). The main idea is to only use RK and T- moves.<br> <br />
For example,<br><br />
<ol><br />
<li>On a 3^3, you can do the sune algorithm: R U R' U R U2 R'. This is an OLL algorithm that can be used to orient corners, but is also able to permute edges (while breaking corners).<br />
</li><br />
<li>On a 3^4, if you replace the algorithm above like so: R=RU, U=TU, you can see that the algorithm seems to have moved 3x1x1x1 blocks. That means that 2c, 3c and 4c are all moved. What if you only want to affect the 3c and 4c of the top 3x3x1x1 block of the T cell? (aka the TU ridge)<br />
</li><br />
<li>Well, back on the 3^3, you can execute sune by doing only R turns and cube rotations. This becomes R z R z' R' z R z' R z R2 z' R'. Notice that the z turn brings the U face into the position of the R face, and the z' turn brings back the original R face.<br />
</li><br />
<li>Now to convert the 3^3 algorithm from the previous step into an RKT algorithm, just substitute R=RK and z=TF. Notice how the T cell seems to be affected in the exact same way the 3^3 was affected in the last step; treating the T cell as a 3^3, it seems to undergo z and R turns. <br />
</li><br />
</ol><br><br />
Note that even though this method is called RKT, it is not limited to those types of turns. Thus, you can use LK and T- moves instead, or rotate your view and use RU and D- instead of RK and T-!<br />
<br />
==Roice's Method==<br />
Roice's Method is a piece-by-piece solution that uses commutators that successively build on each other to solve one type of piece at a time.<br />
A link to the method can be found here.<br />
[http://www.superliminal.com/cube/solution/solution.htm Ultimate Solution to a 3x3x3x3.] <br><br />
<br />
Additionally, Charles Doan has developed a system to implement this method. The tutorials can be found [https://m.youtube.com/playlist?list=PLt_EqFtx5iHwBkNDgqpdX8oVoRuUJejzR here.] <br><br />
<br />
==Sheerin-Zhao Method (Hybrid) V1==<br />
This method is an attempt to make a 4D analogue of the Fridrich/CFOP method. Using this method results in around 650 to 900 moves, even if no shortcut turns are used. This method needs significant improvement because of the move count required for the last layer. <br />
<br />
===Prerequisites===<br />
<ul><br />
<li>Knowledge of how the cube rotates.</li><br />
<li>The Fridrich Method (F2L/OLL/PLL). 2-look OLL/PLL is enough.</li><br />
<li>Some commutators, especially the monoflip. (R' D' R D R' D R and its inverse)</li><br />
<li>The notation described above</li><br />
</ul><br />
===Summary of the Method===<br />
<ol><br />
<li>Cross: Make a cross by solving 8 2C pieces on the far cell.</li><br />
<li>F2L: Fill in F2L slots by joining F2L pairs (2C/3C) together and inserting them into their respective slots.</li><br />
<li>S2L: Fill in S2L slots. This is done by moving a 3C piece and its respective 4C piece onto the farthest cell. Then, OLL algorithms are used to orient the pieces so that they can be joined using RKT moves. They are then inserted using modified RKT moves.</li><br />
<li>OLL: Orient the LL 2C pieces, 3C pieces, ''then'' the 4C pieces using OLL-C (corner OLL) algorithms, such as the sune/antisune. Try to get as many corners oriented as possible as well. Setup moves are highly recommended here.</li><br />
<li>Pre-PLL: Permute the 2C of the LL using U-perms. </li><br />
<li>PLL: Solve the LL like a 3^3 by using RKT moves. (The cube is rotated at this stage)</li><br />
<li>Parity: If the "top face" of the LL is 180 degrees off from the rest of the puzzle, use the RKT variant of the 180-degree-CW supercube center algorithm (R U R' U five times, OR L R U2 R' L' U twice).</li><br />
</ol><br />
<br />
===Method===<br />
====Cross====<br />
<ol><br />
<li>Pick the colour that you will be using for the near cell (the cell not inside the viewpoint). In this example, cyan is chosen.</li><br />
<li>Rotate the puzzle so that the cell with that specified colour is now the near cell.</li><br />
<li>Intuitively place all -K (2C face) pieces oriented and permuted correctly.<br><br />
This image shows the solved cross.<br />
<br>[[File:C2.png|400px]]<br />
</li><br />
</ol><br />
<br />
====F2L====<br />
<ol><br />
<li>Find any 2C piece that does not include a sticker with the colour of the far cell (i.e. grey).</li><br />
<li>Find the 3C piece with the stickers that have the same colours of the 2C piece and of the near cell. For example, if the 2C piece's colours were red and yellow and the near cell piece was cyan, the 3C piece would be red, yellow, and cyan.</li><br />
<li>Intuitively align the two pieces so that they lie on the same slice on the far cell.</li><br />
<li>Join the pair together and insert the pair into the slot using -U moves.</li><br />
<li>Repeat 11 more times. <br>Note: It is possible to insert the slot flipped. There are many shortcuts in forming pairs too. The image below shows the flipped pair (white-blue).<br />
<br>[[File:C3a.png|400px]]<br />
</li><br />
<li>Here is what it should look like when you are done:<br />
<br>[[File:C3b.png|400px]]</li><br />
</ol><br />
<br />
====S2L====<br />
<ol><br />
<li>Find any 3C piece that does not include a sticker with the colour of the far cell (i.e. grey).</li><br />
<li>Find its respective 4C piece (see F2L for details).<br><br />
note: try finding pairs that are already on the far cell first.</li><br />
<li>If either piece is already inserted and there are no more pairs on the far cell, go down to step 6 and use the algorithm to take the piece out of the slot.</li><br />
<li>Orient the pieces so that the same colours are on the far cell. Sune and antisune is used. Setup moves and RKT are a must.</li><br />
<li>Join the pair together using RKT moves. Twist the far cell until the pair is aligned as shown below (i.e. the green-orange-white pair on the D cell):<br><br />
[[File:C4a.png|400px]]<br><br />
It is possible for the pair to be oriented in two other ways. Make sure that the side colours of the S2L pair match the colours of the faces. Notice how the green and orange stickers match up with the side.<br />
<li>Now, the piece can be inserted using RKT. In this case, it is in the form of RU and D- instead of RK and T-, since you are treating the D cell as a 3^3. In the example shown above, since it is to the left of the slot from that viewpoint, it can be inserted using: (LU DT LU' DT') (LU' DT LU DT'). The next image shows the pair in place.<br><br />
[[File:C4b.png|400px]]</li><br />
<li>Repeat 7 more times.</li><br />
<li>Here is what it should look like when you are done (By now you should have used at most 450 moves):<br><br />
[[File:C4c.png|400px]]</li><br />
</ol><br />
<br />
====OLL====<br />
<ol><br />
<li>Use -U variants of OLL algorithms to orient the 2C pieces. (e.g. for line, FU RU TU RU' TU' FU')<br><br />
Attempt to orient as many 3C pieces in this step as possible.</li><br />
<li>For any unoriented 3C pieces, orient them using -U variants of corner OLL algorithms such as the sune.<br><br />
Note: if there is only one 3c piece left unoriented (see image below), place it so that it's facing you (see f2l flipped pair pic for reference). <br><br />
Use this algorithm if the piece needs to rotate CW: [RK2 RU' TR2 TU' LT2 LU' TR2 TU']*2. For rotating the other way, just reverse the algorithm.<br><br />
[[File:C5a.png|400px]]</li><br />
<br><br />
<li>Before starting to orient the 4C pieces, rotate the cube so that the up cell is now the far cell (T->U). The next image shows the transformation. (Notice the unoriented 3C piece. That is an error; orient all 3C pieces first!)<br><br />
[[File:C5b.png|400px]]</li><br />
<li>Do U- moves so that the unoriented 4C pieces have their U cell sticker (i.e. grey sticker) NOT on the T cell.</li> <br />
<li>Use RKT variants of corner OLL algorithms to orient the 4C piece. If by the end of the algorithm the right cell isn't aligned with the rest of the puzzle, do TF, turn RK until the right slice realigns, then do TF'. Repeat this step and the previous one until all 4C pieces are oriented.</li><br />
<li>If there is only one 4C piece left unoriented (see image below), place it so that it's facing you (see f2l flipped pair pic for reference). <br><br />
[[File:C5d.png|400px]]<br><br />
Then, do BR', use the RKT variant of the monoflip, and do BR. The monoflip to rotate the U-layer sticker of the FULT piece from the L cell to the U cell is as shown: [R U R' U']*2 L' [U R U' R']*2 L. Do the inverse for the algorithm that rotates the U-layer sticker of the FULT piece from the F cell to the U cell.<br />
</li><br />
<li>When all LL layer pieces have been oriented, the T cell should be one uniform colour. Rotate the puzzle back (U->T). The image below shows the unrotated puzzle.<br />
[[File:C5e.png|400px]]<br />
</li><br />
</ol><br />
<br />
====PLL====<br />
<ol><br />
<li>Do T- moves to match as many 2C pieces as possible (At least 2). Then use the -U variant of the U perms to match the rest. (See the first step of OLL for an example of a -U variant.)<br><br />
[[File:C6a.png|400px]]</li><br />
</li><br />
<li>From here, you use RKT moves to solve the rest of the puzzle like a 3^3. Parity: If the "top face" of the LL is 180 degrees off from the rest of the puzzle, use the RKT variant of the 180-degree-CW supercube center algorithm (R U R' U five times, OR L R U2 R' L' U twice).</li><br />
</ol><br/><br />
Please note that this step is very inefficient and can take up to 200 moves on its own.<br />
==Charles Doanâ€™s Method==<br />
This method consists of blockbuilding, as well as techniques from Roice Nelsonâ€™s method to solve the last few pieces. The method was intended for a low move count, as well as simply to serve as a unique method to solve the 4 dimensional Rubikâ€™s Cube. Using this method as a beginner is strongly advised against. There will be complex concepts that will be very difficult to grasp, therefore it is advised that this method only be utilized by individuals who have relatively proficient experience for the 3^4 cube. This method will be making use of the notation established by Raymond Zhao.<br />
<br />
===Prerequisites===<br />
<ol><br />
<li> To know how to solve the 4D Rubikâ€™s Cube using Roice Nelsonâ€™s method.<br />
<li> To be proficient at blockbuilding on a normal Rubikâ€™s Cube.<br />
<li> To have adequate experience for the 4D Rubikâ€™s Cube.<br />
</ol><br />
===Steps===<br />
<ol><br />
<li> Solve a 2*2*2*2 cube.<br />
<li> Expand the block to a 2*2*3*2.<br />
<li> Create a full or semi-F2L on the inner face.<br />
<li> Solve the First 2 Layers with or without missing 4-coloreds.<br />
<li> Solve the remaining pieces using Roice Nelsonâ€™s piece-by-piece method or Raymond Zhaoâ€™s OLL/PLL approach.<br />
</ol><br />
<br />
==Octachoroux Method==<br />
This method is Rowan Fortier's 4 dimensional equivalent of the Roux method. It aims for a more intuitive blockbuilding approach, and requires fewer algorithms that need to be memorized. The name Octachoroux comes from the word octachoron (which is another word for tesseract) and Roux.<br />
<br />
===Prerequisites===<br />
<ul><br />
<li> Knowledge of how the puzzle turns, and Zhao Notation </li><br />
<li> Knowledge of blockbuilding and the Roux method on the 3^3 </li><br />
<li> Knowledge of names of 4d pieces and the concept of RKT </li><br />
</ul><br />
<br />
===Summary of the Method:===<br />
<ul><br />
<li> First Block: Solve a 1x2x3x3 block using blockbuilding techniques </li><br />
<li> Second Block: Solve a 1x2x3x3 on the other side of the puzzle to complete your First 2 Blocks </li><br />
<li> CMLC: Orient and permute the corners of the U cell </li><br />
<li> L/R: Solve the Left and Right cells </li><br />
<li> M Slice: Permute the M slice </li><br />
</ul><br />
<br />
===First Block===<br />
Pick the colour of which first block you will be starting with. If you normally start with White or Yellow on D and any colour on the side, that would make you x2yw colour neutral. <br><br />
Build a 1x2x3x3 block. You could solve the 2c pieces first, and then use the K cell to easily pair up pieces without disturbing your progress on the T cell. Then you can just bring those pairs onto the T cell and insert them using -K moves as normal 3^3 twists. <br><br />
Once this step is completed, hold the first block on the left, just as in normal Roux. <br><br />
[[File:Firstblock_2.png|400px]] [[File:Firstblock_1.png|400px]]<br />
<br />
===Second Block===<br />
Make the same 1x2x3x3 block, just on the other side. Start with the DR 2c piece. After that you can solve the other 4 2c pieces by bringing them to TU and doing RF TF' RF' to insert them. You can use many of the same tricks from the 3^3, such as hiding an edge in TDF and then rotating the U cell to bring the corner the edge pairs up with onto the T cell, then connecting them with M moves. RKT is necessary to insert pairs without messing up the first block. <br><br />
[[File:Secondblock.png|400px]]<br />
<br />
===CMLC (CO)===<br />
Bring the U cell to T, then use RKT to set up a layer so that it looks like a normal OCLL case, then bring the T cell to U. Hold that case so that it is in the D layer of the U cell, as shown in the image below, and use RKT variants of OCLL algorithms to orient those pieces. <br><br />
[[File:CMLC_CO1.png|400px]] <br><br />
Repeat this until all the corners are oriented. If you just have 1 corner left to twist, a good intuitive way to do this is to untwist 2 other corners, then use RKT to set that up in to a Sune case. You can also use the Monoflip algorithm described in the Sheerin-Zhao method above. <br><br />
[[File:CMLC_CO2.png||400px]]<br />
<br />
===CMLC (CP)===<br />
Now bring the U cell to T and use RKT to permute it like a regular 2x2x2 Rubik's cube. If you get a parity where a layer ends up being off by 180 degrees, use the RKT parity algorithm: <br><br />
TU UR T[LFU]' UK' TF RF UR RF' U[TR] <br><br />
It will look like this when it is done. Rotate the T cell back to the U cell <br><br />
[[File:CMLC_CP2.png|400px]]<br />
<br />
===L/R===<br />
Instead of orienting the edges like in 3^3 Roux, just go directly to solving the Left and Right cells of the cube. The reason why will become apparent later. <br><br />
First solve the 2c pieces with the L/R and U colour. <br><br />
Now you setup edges that need to go to L/R into the TDF spot with the L/R colour on the T cell and the U colour on the D cell. Then move the spot where that L/R edge needs to go above that edge and insert that piece using the RKT algorithm of M D2 M' D2 (2RK' TF' RK2 TF 2RK TF' RK2 TF) <br><br />
[[File:LR2.png|400px]] <br><br />
There are 8 edges total that need to be inserted for L/R do be complete.<br />
<br />
===M slice===<br />
[[File:M1.png|400px]] <br><br />
Now all you have to do is permute the M slice. This step is pretty similar to PLL from Sheerin-Zhao method, but with some key differences. <br><br />
<ul><br />
<li> Pieces have the same number of colours as they do on the 3^3. Corners pieces have 3, edges have 2, etc. </li><br />
<li> Pieces can look "mirrored" </li><br />
<li> There is no RKT parity </li><br />
</ul><br />
Now you can either use UR moves as U, U', U2 moves, and M slice rotations to do RKT (called URM), or rotate to bring one of the L/R sides to the T cell and use normal RKT, except you have to hold down 2 on your keyboard in order to do T moves. <br><br />
There are some interesting "parities" you might encounter that are impossible on both the 3^3, and the 3^3 last layer of CFOP 3^4. Such as: <br><br />
<ul><br />
<li> Corner pieces that look "mirrored" </li><br />
<li> Impossible Last Layer/CMLL(/whatever method you use) cases </li><br />
</ul><br />
If you solve the M slice using CFOP, then once you get to PLL, you can rotate the puzzle so that the U cell goes to T, and then orient the edges onto the T cell and then permute that like step 4c of the Roux method. <br><br />
If you solve the M slice using Roux, then look forward to impossible CO and CP cases from 2-look CMLL. <br><br />
An algorithm that is super useful here is a pure 2-flip of 3c pieces. I use M' U M' U M' U M' U2 M' U M' U M' U M' using RKT.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_2%5E4_Records&diff=3440Physical 2^4 Records2022-08-13T07:59:21Z<p>Blobinati: </p>
<hr />
<div>This page contains the unofficial records for timed speed solves of Melinda's Physical 2x2x2x2. Add your accomplishments to the tables below, following the existing patterns. You are honor bound to be accurate in your claims. Please add a link to your solve video.<br />
<br />
<br />
<br /><br />
<center><br />
{|border="1" cellpadding="5"<br />
|-<br />
!colspan="3"|Two Handed<br />
!colspan="3"|One Handed<br />
!colspan="3"|BLD<br />
|-<br />
!Date||Name||Time||Date||Name||Time||Date||Name||Time<br />
|-<br />
|2019/8/11||Connor Lindsay||[[https://www.youtube.com/watch?v=oEdrWPEsKPQ 2:26]]<br />
| || || <br />
|2022/08/08||Asa Kaplan||[[https://www.youtube.com/watch?v=lBssOimXaFE 47:14]]<br />
|-<br />
|2021/11/15||Rowan Fortier||[[https://youtu.be/mgfhSL2fi7E 2:16.538]]<br />
|-<br />
|2021/12/6||Rowan Fortier||[[https://youtu.be/tOaBQs34oB0 2:05.27]]<br />
|-<br />
|2021/12/9||Rowan Fortier||[[https://youtu.be/I9hnsif4ImE 2:03.582]]<br />
|-<br />
|2021/12/11||Rowan Fortier||[[https://youtu.be/2SWo0zMlg8I 2:00.656]]<br />
|-<br />
|2021/12/11||Rowan Fortier||[[https://youtu.be/JJPJ7hgNLJU 1:56.748]]<br />
|-<br />
|2022/05/07||Rowan Fortier||[[https://youtu.be/RuUc26S5xpw 1:46.24]]<br />
|-<br />
|2022/06/20||Rowan Fortier||[[https://youtu.be/FSpuv9FJorw 1:28.14]]<br />
|-<br />
|2022/08/02||Rowan Fortier||[[https://youtu.be/XDW7wi4ryPE 1:27.17]]<br />
|-<br />
|2022/08/07||Grant S||[[https://www.youtube.com/watch?v=uEnk2yrJN7I 1:23.28]]<br />
|-<br />
|2022/08/12||Grant S||[[https://www.youtube.com/watch?v=X_FY-CUfvUI 1:07.57]]<br />
|}<br />
<br />
</center></div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_2%5E4_Records&diff=3439Physical 2^4 Records2022-08-13T07:57:54Z<p>Blobinati: </p>
<hr />
<div>This page contains the unofficial records for timed speed solves of Melinda's Physical 2x2x2x2. Add your accomplishments to the tables below, following the existing patterns. You are honor bound to be accurate in your claims. Please add a link to your solve video.<br />
<br />
<br />
<br /><br />
<center><br />
{|border="1" cellpadding="5"<br />
|-<br />
!colspan="3"|Two Handed<br />
!colspan="3"|One Handed<br />
!colspan="3"|BLD<br />
|-<br />
!Date||Name||Time||Date||Name||Time||Date||Name||Time<br />
|-<br />
|2019/8/11||Connor Lindsay||[[https://www.youtube.com/watch?v=oEdrWPEsKPQ 2:26]]<br />
| || || <br />
|2022/08/08||Asa Kaplan||[[https://www.youtube.com/watch?v=lBssOimXaFE 47:14]]<br />
|-<br />
|2021/11/15||Rowan Fortier||[[https://youtu.be/mgfhSL2fi7E 2:16.538]]<br />
|-<br />
|2021/12/6||Rowan Fortier||[[https://youtu.be/tOaBQs34oB0 2:05.27]]<br />
|-<br />
|2021/12/9||Rowan Fortier||[[https://youtu.be/I9hnsif4ImE 2:03.582]]<br />
|-<br />
|2021/12/11||Rowan Fortier||[[https://youtu.be/2SWo0zMlg8I 2:00.656]]<br />
|-<br />
|2021/12/11||Rowan Fortier||[[https://youtu.be/JJPJ7hgNLJU 1:56.748]]<br />
|-<br />
|2022/05/07||Rowan Fortier||[[https://youtu.be/RuUc26S5xpw 1:46.24]]<br />
|-<br />
|2022/06/20||Rowan Fortier||[[https://youtu.be/FSpuv9FJorw 1:28.14]]<br />
|-<br />
|2022/08/02||Rowan Fortier||[[https://youtu.be/XDW7wi4ryPE 1:27.17]]<br />
|-<br />
|2022/08/07||Grant S||[[https://www.youtube.com/watch?v=uEnk2yrJN7I 1:23.28]]<br />
|-<br />
|2022/08/12||Grant S||[[https://www.youtube.com/watch?v=X_FY-CUfvUI 1:07.57]]<br />
<br />
<br />
|}<br />
<br />
</center></div>Blobinatihttp://wiki.superliminal.com/index.php?title=Physical_2%5E4_Records&diff=3438Physical 2^4 Records2022-08-13T07:26:25Z<p>Blobinati: Created page with "This page contains the unofficial records for timed speed solves of Melinda's Physical 2x2x2x2. Add your accomplishments to the tables below, following the existing patterns...."</p>
<hr />
<div>This page contains the unofficial records for timed speed solves of Melinda's Physical 2x2x2x2. Add your accomplishments to the tables below, following the existing patterns. You are honor bound to be accurate in your claims. Please add a link to your solve video.<br />
<br />
<br />
<br /><br />
<center><br />
{|border="1" cellpadding="5"<br />
|-<br />
!colspan="3"|<big>2x2x2x2</big><br />
|-<br />
!Date||Name||Time<br />
|-<br />
|2019/8/11||Connor Lindsay||[[https://www.youtube.com/watch?v=oEdrWPEsKPQ 2:26]]<br />
|-<br />
|2021/11/15||Rowan Fortier||[[https://youtu.be/mgfhSL2fi7E 2:16.538]]<br />
|-<br />
|2021/12/6||Rowan Fortier||[[https://youtu.be/tOaBQs34oB0 2:05.27]]<br />
|-<br />
|2021/12/9||Rowan Fortier||[[https://youtu.be/I9hnsif4ImE 2:03.582]]<br />
|-<br />
|2021/12/11||Rowan Fortier||[[https://youtu.be/2SWo0zMlg8I 2:00.656]]<br />
|-<br />
|2021/12/11||Rowan Fortier||[[https://youtu.be/JJPJ7hgNLJU 1:56.748]]<br />
|-<br />
|2022/05/07||Rowan Fortier||[[https://youtu.be/RuUc26S5xpw 1:46.24]]<br />
|-<br />
|2022/06/20||Rowan Fortier||[[https://youtu.be/FSpuv9FJorw 1:28.14]]<br />
|-<br />
|2022/08/02||Rowan Fortier||[[https://youtu.be/XDW7wi4ryPE 1:27.17]]<br />
|-<br />
|2022/08/07||Grant S||[[https://www.youtube.com/watch?v=uEnk2yrJN7I 1:23.28]]<br />
|-<br />
|2022/08/12||Grant S||[[https://www.youtube.com/watch?v=X_FY-CUfvUI 1:07.57]]<br />
<br />
|}<br />
<br />
</center></div>Blobinatihttp://wiki.superliminal.com/index.php?title=Main_Page&diff=3437Main Page2022-08-13T06:59:57Z<p>Blobinati: </p>
<hr />
<div>==MagicCube4D==<br />
[[File:classic-hypercube.png|thumbnail|left|350px|MagicCube4D]]<br />
<br /><br />
<big>'''MagicCube 4D'''</big><br />
[http://www.superliminal.com/cube/cube.htm]<br />
<br />
For the the 4-dimensional cube puzzle accomplishments, records, and documentation, see [[MagicCube4D]].<br />
<br> <br /><br />
<big>'''Records (first and shortest)'''</big><br />
<br />
For First and Shortest check [[MC4D_Records]].<br />
<br> <br /><br />
<big>'''Gallery'''</big><br />
<br />
Check amazing pictures in [[Image_gallery]].<br />
<br><br/><br />
<big>'''Solutions'''</big><br />
<br />
Solving tips and ideas for other solutions for 4D puzzles click [[MC4D_Solutions]].<br />
<br><br/><br />
<big>'''Join this wiki community'''</big><br />
<br />
To participate in wiki editing, [[Create_Account|create an account]].<br />
<br> <br /><br />
<br> <br /><br />
<br />
==MagicTile==<br />
[[File:MagicTile.PNG|thumbnail|left|350px|MagicTile]]<br />
<br />
<br /><br />
<big>'''MagicTile V2'''</big><br />
[http://www.roice3.org/magictile/]<br />
<br /><br /><br />
<big>'''Records (first and shortest)'''</big><br />
<br /><br />
For First and Shortest check [[MagicTile_Records]].<br />
<br><br /> <br />
<big>'''List of Solvers'''</big><br />
<br /> <br />
For MagicTile v2 Solutions check [[MagicTile v2 Solutions]].<br />
<br> <br /><br />
<big>'''Mathologer Challenge'''</big><br />
<br /> <br />
See the first 100 solvers of the Klein Bottle Rubik's Analogue [[http://roice3.org/magictile/mathologer/ here]].<br />
<br> <br /><br />
<br />
<big>'''Tips and ideas</big><br />
<br /> <br />
For solving tips and ideas for MagicTile puzzles click [[MagicTile aspects]].<br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br />
==Magic Puzzle Ultimate==<br />
[[File:MPUlt_v0.3.PNG|thumbnail|left|350px|Magic Puzzle Ultimate]]<br />
<br />
<br /><br />
<big>'''Magic Puzzle Ultimate'''</big><br />
[http://cardiizastrograda.com/astr/MPUlt/]<br />
<br />
<br /><br />
<big>'''Records (first and shortest)'''</big><br />
<br />
For First and Shortest check [[MPUlt_Records]].<br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br />
==Blindfolded Solving==<br />
[[File:BLD.PNG|thumbnail|left|350px|Blindfolded solving]]<br />
<br />
<br /><br />
<big>'''Rules'''</big><br />
<br /><br />
<br />
<big>The rule of a blindfolded solution without macros:</big><br />
<br /><br />
(1) Starting the solve: make a full scramble using any simulator.<br /><br />
(2) Memorization: the solver memorizes the puzzle without making any twist. The solver may change the viewpoint to inspect the whole puzzle. The solver must not take notes (per WCA regulations). <br /><br />
(3) Put on "blindfold": Preferences > Modes > Blindfold <br /><br />
(4) During the solve: now the solver may make twists.<br /><br />
(5) Ending the solve: a successful solution ends automatically. The duration of the solution includes both the memorization phase and the solving phase.<br />
<br /><br />
<br />
<big>The rule of a blindfolded solution with macros:</big> <br />
<br /><br />
As same as the rule without macros, except: before step (1) the solver may define macros, and during step (4) the solver may use the predefined macros.<br />
<br />
<br /><br />
<br />
<big>'''Records'''</big><br />
<br /><br />
Check [[BLD_Records]].<br />
<br />
<br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br />
==Permutations==<br />
[[File:MC7Dimage.PNG|thumbnail|left|350px|MagicCube7D]]<br />
<br />
<br /><br />
<big>'''Puzzle Index'''</big><br />
<br />
Find permutation counts of every puzzle with explanations in [[Permutations_Index]].<br />
<br> <br /><br />
<big>'''Notation'''</big><br />
<br />
For a description of the notation used in the permutation count explanations, visit [[Permutations_Notation]].<br />
<br/><br />
<br> <br/><br />
<br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br />
==Physical Puzzles==<br />
[[File:Physical3333.jpg|thumbnail|left|350px|Grant's Physical 3x3x3x3]]<br />
<br> <br/><br />
<br />
<big>'''Melinda's Physical 2x2x2x2''' </big><br />
<br> <br/><br />
In 2016, Melinda Green began making the first ever physical representation of a 4D puzzle, the 2^4. Check out her page [[https://superliminal.com/cube/2x2x2x2/ here]].<br />
<br><br/><br />
For different solving methods, visit [[Physical 2^4 Methods]]. <br><br />
For speedsolving records, visit [[Physical 2^4 Records]]<br />
<br />
<br> <br/><br />
<br />
<big>'''Grant's Puzzles''' </big><br />
<br><br/><br />
Grant designed and 3D printed his own puzzles based on Melinda's 2x2x2x2 piece design. He made a 2x2x2x3, 2x2x3x3, 3x3x3x2, and the holy grail, the 3x3x3x3.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=Main_Page&diff=3436Main Page2022-08-13T06:53:22Z<p>Blobinati: </p>
<hr />
<div>==MagicCube4D==<br />
[[File:classic-hypercube.png|thumbnail|left|350px|MagicCube4D]]<br />
<br /><br />
<big>'''MagicCube 4D'''</big><br />
[http://www.superliminal.com/cube/cube.htm]<br />
<br />
For the the 4-dimensional cube puzzle accomplishments, records, and documentation, see [[MagicCube4D]].<br />
<br> <br /><br />
<big>'''Records (first and shortest)'''</big><br />
<br />
For First and Shortest check [[MC4D_Records]].<br />
<br> <br /><br />
<big>'''Gallery'''</big><br />
<br />
Check amazing pictures in [[Image_gallery]].<br />
<br><br/><br />
<big>'''Solutions'''</big><br />
<br />
Solving tips and ideas for other solutions for 4D puzzles click [[MC4D_Solutions]].<br />
<br><br/><br />
<big>'''Join this wiki community'''</big><br />
<br />
To participate in wiki editing, [[Create_Account|create an account]].<br />
<br> <br /><br />
<br> <br /><br />
<br />
==MagicTile==<br />
[[File:MagicTile.PNG|thumbnail|left|350px|MagicTile]]<br />
<br />
<br /><br />
<big>'''MagicTile V2'''</big><br />
[http://www.roice3.org/magictile/]<br />
<br /><br /><br />
<big>'''Records (first and shortest)'''</big><br />
<br /><br />
For First and Shortest check [[MagicTile_Records]].<br />
<br><br /> <br />
<big>'''List of Solvers'''</big><br />
<br /> <br />
For MagicTile v2 Solutions check [[MagicTile v2 Solutions]].<br />
<br> <br /><br />
<big>'''Mathologer Challenge'''</big><br />
<br /> <br />
See the first 100 solvers of the Klein Bottle Rubik's Analogue [[http://roice3.org/magictile/mathologer/ here]].<br />
<br> <br /><br />
<br />
<big>'''Tips and ideas</big><br />
<br /> <br />
For solving tips and ideas for MagicTile puzzles click [[MagicTile aspects]].<br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br> <br /><br />
<br />
==Magic Puzzle Ultimate==<br />
[[File:MPUlt_v0.3.PNG|thumbnail|left|350px|Magic Puzzle Ultimate]]<br />
<br />
<br /><br />
<big>'''Magic Puzzle Ultimate'''</big><br />
[http://cardiizastrograda.com/astr/MPUlt/]<br />
<br />
<br /><br />
<big>'''Records (first and shortest)'''</big><br />
<br />
For First and Shortest check [[MPUlt_Records]].<br />
<br> <br /><br />
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==Blindfolded Solving==<br />
[[File:BLD.PNG|thumbnail|left|350px|Blindfolded solving]]<br />
<br />
<br /><br />
<big>'''Rules'''</big><br />
<br /><br />
<br />
<big>The rule of a blindfolded solution without macros:</big><br />
<br /><br />
(1) Starting the solve: make a full scramble using any simulator.<br /><br />
(2) Memorization: the solver memorizes the puzzle without making any twist. The solver may change the viewpoint to inspect the whole puzzle. The solver must not take notes (per WCA regulations). <br /><br />
(3) Put on "blindfold": Preferences > Modes > Blindfold <br /><br />
(4) During the solve: now the solver may make twists.<br /><br />
(5) Ending the solve: a successful solution ends automatically. The duration of the solution includes both the memorization phase and the solving phase.<br />
<br /><br />
<br />
<big>The rule of a blindfolded solution with macros:</big> <br />
<br /><br />
As same as the rule without macros, except: before step (1) the solver may define macros, and during step (4) the solver may use the predefined macros.<br />
<br />
<br /><br />
<br />
<big>'''Records'''</big><br />
<br /><br />
Check [[BLD_Records]].<br />
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==Permutations==<br />
[[File:MC7Dimage.PNG|thumbnail|left|350px|MagicCube7D]]<br />
<br />
<br /><br />
<big>'''Puzzle Index'''</big><br />
<br />
Find permutation counts of every puzzle with explanations in [[Permutations_Index]].<br />
<br> <br /><br />
<big>'''Notation'''</big><br />
<br />
For a description of the notation used in the permutation count explanations, visit [[Permutations_Notation]].<br />
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==Physical Puzzles==<br />
[[File:Physical3333.jpg|thumbnail|left|350px|Grant's Physical 3x3x3x3]]<br />
<br> <br/><br />
<br />
<big>'''Melinda's Physical 2x2x2x2''' </big><br />
<br> <br/><br />
In 2016, Melinda Green began making the first ever physical representation of a 4D puzzle, the 2^4. Check out her page [[https://superliminal.com/cube/2x2x2x2/ here]].<br />
<br><br/><br />
For different solving methods, visit [[Physical 2^4 Methods]].<br />
<br />
<br> <br/><br />
<br />
<big>'''Grant's Puzzles''' </big><br />
<br><br/><br />
Grant designed and 3D printed his own puzzles based on Melinda's 2x2x2x2 piece design. He made a 2x2x2x3, 2x2x3x3, 3x3x3x2, and the holy grail, the 3x3x3x3.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=File:Physical3333.jpg&diff=3435File:Physical3333.jpg2022-08-13T06:38:47Z<p>Blobinati: </p>
<hr />
<div></div>Blobinatihttp://wiki.superliminal.com/index.php?title=MC4D_Solutions&diff=3396MC4D Solutions2021-11-04T01:13:52Z<p>Blobinati: </p>
<hr />
<div><br />
[[3^4|{4,3,3} 3: 3 Layer Tesseract]] <br /><br />
[[2^4| {4,3,3} 3: 2 Layer Tesseract]] <br /><br />
[[2 Layer Simplex|{3,3,3} 2: 2 Layer Simplex]] <br /><br />
[[Luna%27s_Duoprism_Method|{N}x{4} Duoprisms]]</div>Blobinatihttp://wiki.superliminal.com/index.php?title=2%5E4&diff=33952^42021-11-04T01:11:41Z<p>Blobinati: Created page with "Many of the techniques used on the 3x3x3x3 also apply to the 2x2x2x2. ==Cell By Cell Method== This is the 4-dimensional equivalent to the Layer By Layer method on the 2x2x2. =..."</p>
<hr />
<div>Many of the techniques used on the 3x3x3x3 also apply to the 2x2x2x2.<br />
==Cell By Cell Method==<br />
This is the 4-dimensional equivalent to the Layer By Layer method on the 2x2x2.<br />
===Solve a cell===<br />
This can be done either by just orienting the cell first, then putting that cell at I and using -O moves to permute the pieces of it around, or by using direct blockbuilding to solve the pieces.<br />
===Orient Last Cell===<br />
Similar to OLL, in this step the solver orients all 8 corners of the U cell so that the U colour is on the U cell. This can be done with RKT setup moves to create familiar 2x2x2 OCLL cases, then 4d rotating to use RKT on a different cell to orient those corners. Another strategy is to pair up 2x2x1(x1) blocks or oriented corners, and permute those using -U variants of OCLL algorithms.<br />
===Permute Last Cell===<br />
For the final step, permute the last cell just like a regular 2x2x2 Rubik's Cube. You will have to use RKT to do this. There is a 50% chance of RKT parity occurring, which you will need an algorithm to fix.<br />
<br />
==Ortega Method==<br />
This is the 4-dimensional equivalent to the Ortega method on the 2x2x2.<br />
===Orient a cell===<br />
Orient a cell.<br />
===Orient Last Cell===<br />
Similar to OLL, in this step the solver orients all 8 corners of the U cell so that the U colour is on the U cell. But because the First Cell was not permuted, you don't have to use RKT in order to orient it (though it can be certainly helpful), which saves a few moves.<br />
===Permute Both Cells===<br />
Now just permute both of the cells like normal 2x2x2x cubes. For the first cell, you don't have to use and RKT because you can just put the first cell at I and use -O moves to turn its sides. For the Last Cell, you will have to use RKT.<br />
<br />
==Luna's Physical 2x2x2x2 Method==<br />
This method works really well on Melinda's Physical 2x2x2x2 puzzle [https://superliminal.com/cube/2x2x2x2/] , but it can be used on the virtual 2x2x2x2 as well. <br />
===Domino Reduction===<br />
Orient 2 opposite cells of the puzzle, but they can be oriented with either colour.<br />
===Permute First Cell===<br />
Treating the whole puzzle like a 2x2x4 domino puzzle (except you can rotate the U/D halves in any direction), solve a cell. This will automatically complete separation of the U/D colours.<br />
===Permute Last Cell===<br />
For the final step, permute the last cell just like a regular 2x2x2 Rubik's Cube. You will have to use RKT to do this. There is a 50% chance of RKT parity occurring, which you will need an algorithm to fix.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=Notation&diff=3394Notation2021-11-02T20:00:43Z<p>Blobinati: </p>
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<div>==n^4:==<br />
===Commonly Used Notations:===<br />
<br />
'''Zhao Notation:''' <br><br />
The notation is similar to that of the 3^3. There are 8 cells, six of them using the same letters as that in the 3^3: U (up), D (down), F (front), B (back), R (right), L (left). The near cell which is not visible, is named K, for kata. The far cell, which appears as the innermost cell, is named T, for top. (''Thanks to Neodam22 for pointing out the problem!'') Its name was changed from A to T since ana and kata are easier to confuse with each other than kata and "top".<br><br />
Each cell in turn uses [http://worldcubeassociation.org/regulations/#notation WCA Official Notation] (standard notation).<br><br />
'''The first letter determines the cell to click on. The second letter determines the sticker on the cell (is usually a 2C piece) to click on''' For example: <br><br />
RK means to click the sticker on the right cell that joins to the near cell.<br><br />
TF means to click the sticker on the far cell that joins to the front cell.<br><br />
FT means to click the sticker on the front cell that joins to the far cell.<br><br />
To state a set of all possible turns (clicks) of a cell, X- is used. For example: R- includes RU, RF, RD, RB, RT, and RK.<br><br />
To state a set of all possible turns (clicks) of cells that are joined to the original sticker to be clicked, -X is used. For example, -R includes UR, FR, DR and BR, TR and KR. <br><br />
Slice and wide turns can be notated with the 2c piece that you click on, plus the number you hold down to perform that move. For example, 2RK is like an M', and 12RK is like Rw'. <br><br />
<br />
'''I/O variant of Zhao Notation''' <br> <br />
Some people in the community prefer to use I (Inner) instead of T, and O (Outer) instead of K. <br> <br />
This makes it more obvious which face is which, whereas "Top" can be confused with Up <br><br />
<br />
'''Rotation Notation:'''<br><br />
Rotation Notation uses the same cell names from Zhao's Notation, but uses 3^3 x, y, and z rotations to be more intuitive. <br><br />
Each turn is made up of the face you click in followed by which rotation that face undergoes. <br><br />
If you wanted to make the F face of the T cell become the U face of the T cell, that would be Tx because it's rotating the T cell clockwise along the x axis. <br><br />
One of the downsides of this notation is that edge and corner twist moves become longer. For example: T[UF] becomes Tz2x. <br><br />
<br />
'''Rotation Notation V2:'''<br><br />
Rotating around an axis is actually just a trope of living in 3 dimensions. It is much more helpful to think about rotations as happening in a 2-dimensional plane rather than around a 1-dimensional axis. This idea became the basis for Rotation Notation V2. <br><br />
In 3d, the rotations are x, y, and z. You can think about these rotations being called this because they are not in the plane. For example, a y rotation is rotating a 3x3x3 within the xz plane, so it is called y. And y is closer in the alphabet to U than it is to D, so a y rotation goes the same way as a U rotation, except to all 3 layers. <br><br />
The same exact logic works in 4d, but this time you have to list the 2 axes that the plane of rotation doesn't involve. For example, doing an RK move would be Rxw because an RK rotates the R cell within the yz plane. And it would go the same direction as R because x is closer in the alphabet to R than L.<br />
<br />
===Experimental Notations:===<br />
<br />
'''Symmetry Notation:''' <br><br />
Blob Notation was an attempt by Blobinati Cuber to make Zhao Notation more efficient by making each of the 13 symmetries of a cube into a letter (a-m) following the main 8 letters that represent the cells. <br> <br />
a, b, & c were y, x, & z rotations, and the rest were various corner and edge twists. <br><br />
This notation does succeed in making corner and edge twist moves take up less letters to write, at the cost of having to memorize 13 new letters and what their moves look like. <br><br />
<br />
'''Picture Notation''' <br><br />
Picture Notation was an attempt by Blobinati Cuber to make Zhao Notation easier to visualize by using little pictures to represent the cells' rotations. If you imagine that you are looking into the inside of a box from one of the faces, then the possible shapes you can see is the small square, the big square, and the 4 trapezoids in-between, which are just squished squares due to the projection of the cube onto 2d space. <br><br />
You start each turn by imagining the letter that represents that cell (U, D, R, L, F, B, T, K) is on the F face. Then, perform the rotations of the cell and draw the letter on the correct shape and orientation to represent where it ended up.<br />
<br />
===Uncommon/old Notations:===<br />
<br />
'''Roice Notation:''' <br><br />
Roice's Notation uses different names for the cells. <br><br />
[[File:RoiceNotation.gif|400px]] <br><br />
Each cell's stickers are numbered from 1-27 like this: <br><br />
[[File:smallNumbers.png|400px]] <br><br />
You then state whether you did a right or left click. Examples: <br><br />
Top, 5, Left <br><br />
Left, 9, Right <br><br />
<br />
===Examples:===<br />
Below are examples of the 9 move RKT parity algorithm in all of the above notations. <br><br />
TU UR T[LFU]' UK' TF RF UR RF' U[TR] <br><br />
IU UR I[LFU]' UO' IF RF UR RF' U[IR] <br><br />
Ty Ux Tz'x Uy' Tz Rz Ux Rz' Ux2z <br></div>Blobinatihttp://wiki.superliminal.com/index.php?title=3%5E4&diff=33883^42021-08-27T04:38:39Z<p>Blobinati: </p>
<hr />
<div>Visit [[Notation]] to get an overview of the different notation systems to describe moves on the 3^4. <br><br />
<br />
===RKT===<br />
RKT is a technique that is used to execute moves that damage fewer pieces. By using RKT, the solver picks a cell that the solver wants to treat i.e. as a 3^3 (If it was a 4^4 you were solving, RKT would treat a cell as a 4^3). The main idea is to only use RK and T- moves.<br> <br />
For example,<br><br />
<ol><br />
<li>On a 3^3, you can do the sune algorithm: R U R' U R U2 R'. This is an OLL algorithm that can be used to orient corners, but is also able to permute edges (while breaking corners).<br />
</li><br />
<li>On a 3^4, if you replace the algorithm above like so: R=RU, U=TU, you can see that the algorithm seems to have moved 3x1x1x1 blocks. That means that 2c, 3c and 4c are all moved. What if you only want to affect the 3c and 4c of the top 3x3x1x1 block of the T cell? (aka the TU ridge)<br />
</li><br />
<li>Well, back on the 3^3, you can execute sune by doing only R turns and cube rotations. This becomes R z R z' R' z R z' R z R2 z' R'. Notice that the z turn brings the U face into the position of the R face, and the z' turn brings back the original R face.<br />
</li><br />
<li>Now to convert the 3^3 algorithm from the previous step into an RKT algorithm, just substitute R=RK and z=TF. Notice how the T cell seems to be affected in the exact same way the 3^3 was affected in the last step; treating the T cell as a 3^3, it seems to undergo z and R turns. <br />
</li><br />
</ol><br><br />
Note that even though this method is called RKT, it is not limited to those types of turns. Thus, you can use LK and T- moves instead, or rotate your view and use RU and D- instead of RK and T-!<br />
<br />
==Roice's Method==<br />
Roice's Method is a piece-by-piece solution that uses commutators that successively build on each other to solve one type of piece at a time.<br />
A link to the method can be found here.<br />
[http://www.superliminal.com/cube/solution/solution.htm Ultimate Solution to a 3x3x3x3.] <br><br />
<br />
Additionally, Charles Doan has developed a system to implement this method. The tutorials can be found [https://m.youtube.com/playlist?list=PLt_EqFtx5iHwBkNDgqpdX8oVoRuUJejzR here.] <br><br />
<br />
==Sheerin-Zhao Method (Hybrid) V1==<br />
This method is an attempt to make a 4D analogue of the Fridrich/CFOP method. Using this method results in around 650 to 900 moves, even if no shortcut turns are used. This method needs significant improvement because of the move count required for the last layer. <br />
<br />
===Prerequisites===<br />
<ul><br />
<li>Knowledge of how the cube rotates.</li><br />
<li>The Fridrich Method (F2L/OLL/PLL). 2-look OLL/PLL is enough.</li><br />
<li>Some commutators, especially the monoflip. (R' D' R D R' D R and its inverse)</li><br />
<li>The notation described above</li><br />
</ul><br />
===Summary of the Method===<br />
<ol><br />
<li>Cross: Make a cross by solving 8 2C pieces on the far cell.</li><br />
<li>F2L: Fill in F2L slots by joining F2L pairs (2C/3C) together and inserting them into their respective slots.</li><br />
<li>S2L: Fill in S2L slots. This is done by moving a 3C piece and its respective 4C piece onto the farthest cell. Then, OLL algorithms are used to orient the pieces so that they can be joined using RKT moves. They are then inserted using modified RKT moves.</li><br />
<li>OLL: Orient the LL 2C pieces, 3C pieces, ''then'' the 4C pieces using OLL-C (corner OLL) algorithms, such as the sune/antisune. Try to get as many corners oriented as possible as well. Setup moves are highly recommended here.</li><br />
<li>Pre-PLL: Permute the 2C of the LL using U-perms. </li><br />
<li>PLL: Solve the LL like a 3^3 by using RKT moves. (The cube is rotated at this stage)</li><br />
<li>Parity: If the "top face" of the LL is 180 degrees off from the rest of the puzzle, use the RKT variant of the 180-degree-CW supercube center algorithm (R U R' U five times, OR L R U2 R' L' U twice).</li><br />
</ol><br />
<br />
===Method===<br />
====Cross====<br />
<ol><br />
<li>Pick the colour that you will be using for the near cell (the cell not inside the viewpoint). In this example, cyan is chosen.</li><br />
<li>Rotate the puzzle so that the cell with that specified colour is now the near cell.</li><br />
<li>Intuitively place all -K (2C face) pieces oriented and permuted correctly.<br><br />
This image shows the solved cross.<br />
<br>[[File:C2.png|400px]]<br />
</li><br />
</ol><br />
<br />
====F2L====<br />
<ol><br />
<li>Find any 2C piece that does not include a sticker with the colour of the far cell (i.e. grey).</li><br />
<li>Find the 3C piece with the stickers that have the same colours of the 2C piece and of the near cell. For example, if the 2C piece's colours were red and yellow and the near cell piece was cyan, the 3C piece would be red, yellow, and cyan.</li><br />
<li>Intuitively align the two pieces so that they lie on the same slice on the far cell.</li><br />
<li>Join the pair together and insert the pair into the slot using -U moves.</li><br />
<li>Repeat 11 more times. <br>Note: It is possible to insert the slot flipped. There are many shortcuts in forming pairs too. The image below shows the flipped pair (white-blue).<br />
<br>[[File:C3a.png|400px]]<br />
</li><br />
<li>Here is what it should look like when you are done:<br />
<br>[[File:C3b.png|400px]]</li><br />
</ol><br />
<br />
====S2L====<br />
<ol><br />
<li>Find any 3C piece that does not include a sticker with the colour of the far cell (i.e. grey).</li><br />
<li>Find its respective 4C piece (see F2L for details).<br><br />
note: try finding pairs that are already on the far cell first.</li><br />
<li>If either piece is already inserted and there are no more pairs on the far cell, go down to step 6 and use the algorithm to take the piece out of the slot.</li><br />
<li>Orient the pieces so that the same colours are on the far cell. Sune and antisune is used. Setup moves and RKT are a must.</li><br />
<li>Join the pair together using RKT moves. Twist the far cell until the pair is aligned as shown below (i.e. the green-orange-white pair on the D cell):<br><br />
[[File:C4a.png|400px]]<br><br />
It is possible for the pair to be oriented in two other ways. Make sure that the side colours of the S2L pair match the colours of the faces. Notice how the green and orange stickers match up with the side.<br />
<li>Now, the piece can be inserted using RKT. In this case, it is in the form of RU and D- instead of RK and T-, since you are treating the D cell as a 3^3. In the example shown above, since it is to the left of the slot from that viewpoint, it can be inserted using: (LU DT LU' DT') (LU' DT LU DT'). The next image shows the pair in place.<br><br />
[[File:C4b.png|400px]]</li><br />
<li>Repeat 7 more times.</li><br />
<li>Here is what it should look like when you are done (By now you should have used at most 450 moves):<br><br />
[[File:C4c.png|400px]]</li><br />
</ol><br />
<br />
====OLL====<br />
<ol><br />
<li>Use -U variants of OLL algorithms to orient the 2C pieces. (e.g. for line, FU RU TU RU' TU' FU')<br><br />
Attempt to orient as many 3C pieces in this step as possible.</li><br />
<li>For any unoriented 3C pieces, orient them using -U variants of corner OLL algorithms such as the sune.<br><br />
Note: if there is only one 3c piece left unoriented (see image below), place it so that it's facing you (see f2l flipped pair pic for reference). <br><br />
Use this algorithm if the piece needs to rotate CW: [RK2 RU' TR2 TU' LT2 LU' TR2 TU']*2. For rotating the other way, just reverse the algorithm.<br><br />
[[File:C5a.png|400px]]</li><br />
<br><br />
<li>Before starting to orient the 4C pieces, rotate the cube so that the up cell is now the far cell (T->U). The next image shows the transformation. (Notice the unoriented 3C piece. That is an error; orient all 3C pieces first!)<br><br />
[[File:C5b.png|400px]]</li><br />
<li>Do U- moves so that the unoriented 4C pieces have their U cell sticker (i.e. grey sticker) NOT on the T cell.</li> <br />
<li>Use RKT variants of corner OLL algorithms to orient the 4C piece. If by the end of the algorithm the right cell isn't aligned with the rest of the puzzle, do TF, turn RK until the right slice realigns, then do TF'. Repeat this step and the previous one until all 4C pieces are oriented.</li><br />
<li>If there is only one 4C piece left unoriented (see image below), place it so that it's facing you (see f2l flipped pair pic for reference). <br><br />
[[File:C5d.png|400px]]<br><br />
Then, do BR', use the RKT variant of the monoflip, and do BR. The monoflip to rotate the U-layer sticker of the FULT piece from the L cell to the U cell is as shown: [R U R' U']*2 L' [U R U' R']*2 L. Do the inverse for the algorithm that rotates the U-layer sticker of the FULT piece from the F cell to the U cell.<br />
</li><br />
<li>When all LL layer pieces have been oriented, the T cell should be one uniform colour. Rotate the puzzle back (U->T). The image below shows the unrotated puzzle.<br />
[[File:C5e.png|400px]]<br />
</li><br />
</ol><br />
<br />
====PLL====<br />
<ol><br />
<li>Do T- moves to match as many 2C pieces as possible (At least 2). Then use the -U variant of the U perms to match the rest. (See the first step of OLL for an example of a -U variant.)<br><br />
[[File:C6a.png|400px]]</li><br />
</li><br />
<li>From here, you use RKT moves to solve the rest of the puzzle like a 3^3. Parity: If the "top face" of the LL is 180 degrees off from the rest of the puzzle, use the RKT variant of the 180-degree-CW supercube center algorithm (R U R' U five times, OR L R U2 R' L' U twice).</li><br />
</ol><br/><br />
Please note that this step is very inefficient and can take up to 200 moves on its own.<br />
==Charles Doanâ€™s Method==<br />
This method consists of blockbuilding, as well as techniques from Roice Nelsonâ€™s method to solve the last few pieces. The method was intended for a low move count, as well as simply to serve as a unique method to solve the 4 dimensional Rubikâ€™s Cube. Using this method as a beginner is strongly advised against. There will be complex concepts that will be very difficult to grasp, therefore it is advised that this method only be utilized by individuals who have relatively proficient experience for the 3^4 cube. This method will be making use of the notation established by Raymond Zhao.<br />
<br />
===Prerequisites===<br />
<ol><br />
<li> To know how to solve the 4D Rubikâ€™s Cube using Roice Nelsonâ€™s method.<br />
<li> To be proficient at blockbuilding on a normal Rubikâ€™s Cube.<br />
<li> To have adequate experience for the 4D Rubikâ€™s Cube.<br />
</ol><br />
===Steps===<br />
<ol><br />
<li> Solve a 2*2*2*2 cube.<br />
<li> Expand the block to a 2*2*3*2.<br />
<li> Create a full or semi-F2L on the inner face.<br />
<li> Solve the First 2 Layers with or without missing 4-coloreds.<br />
<li> Solve the remaining pieces using Roice Nelsonâ€™s piece-by-piece method or Raymond Zhaoâ€™s OLL/PLL approach.<br />
</ol><br />
<br />
==Octachoroux Method==<br />
This method is Rowan Fortier's 4 dimensional equivalent of the Roux method. It aims for a more intuitive blockbuilding approach, and requires fewer algorithms that need to be memorized. The name Octachoroux comes from the word octachoron (which is another word for tesseract) and Roux.<br />
<br />
===Prerequisites===<br />
<ul><br />
<li> Knowledge of how the puzzle turns, and Zhao Notation </li><br />
<li> Knowledge of blockbuilding and the Roux method on the 3^3 </li><br />
<li> Knowledge of names of 4d pieces and the concept of RKT </li><br />
</ul><br />
<br />
===Summary of the Method:===<br />
<ul><br />
<li> First Block: Solve a 1x2x3x3 block using blockbuilding techniques </li><br />
<li> Second Block: Solve a 1x2x3x3 on the other side of the puzzle to complete your First 2 Blocks </li><br />
<li> CMLC: Orient and permute the corners of the U cell </li><br />
<li> L/R: Solve the Left and Right cells </li><br />
<li> M Slice: Permute the M slice </li><br />
</ul><br />
<br />
===First Block===<br />
Pick the colour of which first block you will be starting with. If you normally start with White or Yellow on D and any colour on the side, that would make you x2yw colour neutral. <br><br />
Build a 1x2x3x3 block. You could solve the 2c pieces first, and then use the K cell to easily pair up pieces without disturbing your progress on the T cell. Then you can just bring those pairs onto the T cell and insert them using -K moves as normal 3^3 twists. <br><br />
Once this step is completed, hold the first block on the left, just as in normal Roux. <br><br />
[[File:Firstblock_2.png|400px]] [[File:Firstblock_1.png|400px]]<br />
<br />
===Second Block===<br />
Make the same 1x2x3x3 block, just on the other side. Start with the DR 2c piece. After that you can solve the other 4 2c pieces by bringing them to TU and doing RF TF' RF' to insert them. You can use many of the same tricks from the 3^3, such as hiding an edge in TDF and then rotating the U cell to bring the corner the edge pairs up with onto the T cell, then connecting them with M moves. RKT is necessary to insert pairs without messing up the first block. <br><br />
[[File:Secondblock.png|400px]]<br />
<br />
===CMLC (CO)===<br />
Bring the U cell to T, then use RKT to set up a layer so that it looks like a normal OCLL case, then bring the T cell to U. Hold that case so that it is in the D layer of the U cell, as shown in the image below, and use RKT variants of OCLL algorithms to orient those pieces. <br><br />
[[File:CMLC_CO1.png|400px]] <br><br />
Repeat this until all the corners are oriented. If you just have 1 corner left to twist, a good intuitive way to do this is to untwist 2 other corners, then use RKT to set that up in to a Sune case. You can also use the Monoflip algorithm described in the Sheerin-Zhao method above. <br><br />
[[File:CMLC_CO2.png||400px]]<br />
<br />
===CMLC (CP)===<br />
Now bring the U cell to T and use RKT to permute it like a regular 2x2x2 Rubik's cube. If you get a parity where a layer ends up being off by 180 degrees, use the RKT parity algorithm: <br><br />
TU UR T[LFU]' UK' TF RF UR RF' U[TR] <br><br />
It will look like this when it is done. Rotate the T cell back to the U cell <br><br />
[[File:CMLC_CP2.png|400px]]<br />
<br />
===L/R===<br />
Instead of orienting the edges like in 3^3 Roux, just go directly to solving the Left and Right cells of the cube. The reason why will become apparent later. <br><br />
First solve the 2c pieces with the L/R and U colour. <br><br />
Now you setup edges that need to go to L/R into the TDF spot with the L/R colour on the T cell and the U colour on the D cell. Then move the spot where that L/R edge needs to go above that edge and insert that piece using the RKT algorithm of M D2 M' D2 (2RK' TF' RK2 TF 2RK TF' RK2 TF) <br><br />
[[File:LR2.png|400px]] <br><br />
There are 8 edges total that need to be inserted for L/R do be complete.<br />
<br />
===M slice===<br />
[[File:M1.png|400px]] <br><br />
Now all you have to do is permute the M slice. This step is pretty similar to PLL from Sheerin-Zhao method, but with some key differences. <br><br />
<ul><br />
<li> Pieces have the same number of colours as they do on the 3^3. Corners pieces have 3, edges have 2, etc. </li><br />
<li> Pieces can look "mirrored" </li><br />
<li> There is no RKT parity </li><br />
</ul><br />
Now you can either use UR moves as U, U', U2 moves, and M slice rotations to do RKT (called URM), or rotate to bring one of the L/R sides to the T cell and use normal RKT, except you have to hold down 2 on your keyboard in order to do T moves. <br><br />
There are some interesting "parities" you might encounter that are impossible on both the 3^3, and the 3^3 last layer of CFOP 3^4. Such as: <br><br />
<ul><br />
<li> Corner pieces that look "mirrored" </li><br />
<li> Impossible Last Layer/CMLL(/whatever method you use) cases </li><br />
</ul><br />
If you solve the M slice using CFOP, then once you get to PLL, you can rotate the puzzle so that the U cell goes to T, and then orient the edges onto the T cell and then permute that like step 4c of the Roux method. <br><br />
If you solve the M slice using Roux, then look forward to impossible CO and CP cases from 2-look CMLL. <br><br />
An algorithm that is super useful here is a pure 2-flip of 3c pieces. I use M' U M' U M' U M' U2 M' U M' U M' U M' using RKT.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=3%5E4&diff=33873^42021-08-27T04:33:03Z<p>Blobinati: </p>
<hr />
<div>Visit [http://wiki.superliminal.com/wiki/Notation this page] to get an overview of the different notation systems to describe moves on the 3^4. <br><br />
<br />
===RKT===<br />
RKT is a technique that is used to execute moves that damage fewer pieces. By using RKT, the solver picks a cell that the solver wants to treat i.e. as a 3^3 (If it was a 4^4 you were solving, RKT would treat a cell as a 4^3). The main idea is to only use RK and T- moves.<br> <br />
For example,<br><br />
<ol><br />
<li>On a 3^3, you can do the sune algorithm: R U R' U R U2 R'. This is an OLL algorithm that can be used to orient corners, but is also able to permute edges (while breaking corners).<br />
</li><br />
<li>On a 3^4, if you replace the algorithm above like so: R=RU, U=TU, you can see that the algorithm seems to have moved 3x1x1x1 blocks. That means that 2c, 3c and 4c are all moved. What if you only want to affect the 3c and 4c of the top 3x3x1x1 block of the T cell? (aka the TU ridge)<br />
</li><br />
<li>Well, back on the 3^3, you can execute sune by doing only R turns and cube rotations. This becomes R z R z' R' z R z' R z R2 z' R'. Notice that the z turn brings the U face into the position of the R face, and the z' turn brings back the original R face.<br />
</li><br />
<li>Now to convert the 3^3 algorithm from the previous step into an RKT algorithm, just substitute R=RK and z=TF. Notice how the T cell seems to be affected in the exact same way the 3^3 was affected in the last step; treating the T cell as a 3^3, it seems to undergo z and R turns. <br />
</li><br />
</ol><br><br />
Note that even though this method is called RKT, it is not limited to those types of turns. Thus, you can use LK and T- moves instead, or rotate your view and use RU and D- instead of RK and T-!<br />
<br />
==Roice's Method==<br />
Roice's Method is a piece-by-piece solution that uses commutators that successively build on each other to solve one type of piece at a time.<br />
A link to the method can be found here.<br />
[http://www.superliminal.com/cube/solution/solution.htm Ultimate Solution to a 3x3x3x3.] <br><br />
<br />
Additionally, Charles Doan has developed a system to implement this method. The tutorials can be found [https://m.youtube.com/playlist?list=PLt_EqFtx5iHwBkNDgqpdX8oVoRuUJejzR here.] <br><br />
<br />
==Sheerin-Zhao Method (Hybrid) V1==<br />
This method is an attempt to make a 4D analogue of the Fridrich/CFOP method. Using this method results in around 650 to 900 moves, even if no shortcut turns are used. This method needs significant improvement because of the move count required for the last layer. <br />
<br />
===Prerequisites===<br />
<ul><br />
<li>Knowledge of how the cube rotates.</li><br />
<li>The Fridrich Method (F2L/OLL/PLL). 2-look OLL/PLL is enough.</li><br />
<li>Some commutators, especially the monoflip. (R' D' R D R' D R and its inverse)</li><br />
<li>The notation described above</li><br />
</ul><br />
===Summary of the Method===<br />
<ol><br />
<li>Cross: Make a cross by solving 8 2C pieces on the far cell.</li><br />
<li>F2L: Fill in F2L slots by joining F2L pairs (2C/3C) together and inserting them into their respective slots.</li><br />
<li>S2L: Fill in S2L slots. This is done by moving a 3C piece and its respective 4C piece onto the farthest cell. Then, OLL algorithms are used to orient the pieces so that they can be joined using RKT moves. They are then inserted using modified RKT moves.</li><br />
<li>OLL: Orient the LL 2C pieces, 3C pieces, ''then'' the 4C pieces using OLL-C (corner OLL) algorithms, such as the sune/antisune. Try to get as many corners oriented as possible as well. Setup moves are highly recommended here.</li><br />
<li>Pre-PLL: Permute the 2C of the LL using U-perms. </li><br />
<li>PLL: Solve the LL like a 3^3 by using RKT moves. (The cube is rotated at this stage)</li><br />
<li>Parity: If the "top face" of the LL is 180 degrees off from the rest of the puzzle, use the RKT variant of the 180-degree-CW supercube center algorithm (R U R' U five times, OR L R U2 R' L' U twice).</li><br />
</ol><br />
<br />
===Method===<br />
====Cross====<br />
<ol><br />
<li>Pick the colour that you will be using for the near cell (the cell not inside the viewpoint). In this example, cyan is chosen.</li><br />
<li>Rotate the puzzle so that the cell with that specified colour is now the near cell.</li><br />
<li>Intuitively place all -K (2C face) pieces oriented and permuted correctly.<br><br />
This image shows the solved cross.<br />
<br>[[File:C2.png|400px]]<br />
</li><br />
</ol><br />
<br />
====F2L====<br />
<ol><br />
<li>Find any 2C piece that does not include a sticker with the colour of the far cell (i.e. grey).</li><br />
<li>Find the 3C piece with the stickers that have the same colours of the 2C piece and of the near cell. For example, if the 2C piece's colours were red and yellow and the near cell piece was cyan, the 3C piece would be red, yellow, and cyan.</li><br />
<li>Intuitively align the two pieces so that they lie on the same slice on the far cell.</li><br />
<li>Join the pair together and insert the pair into the slot using -U moves.</li><br />
<li>Repeat 11 more times. <br>Note: It is possible to insert the slot flipped. There are many shortcuts in forming pairs too. The image below shows the flipped pair (white-blue).<br />
<br>[[File:C3a.png|400px]]<br />
</li><br />
<li>Here is what it should look like when you are done:<br />
<br>[[File:C3b.png|400px]]</li><br />
</ol><br />
<br />
====S2L====<br />
<ol><br />
<li>Find any 3C piece that does not include a sticker with the colour of the far cell (i.e. grey).</li><br />
<li>Find its respective 4C piece (see F2L for details).<br><br />
note: try finding pairs that are already on the far cell first.</li><br />
<li>If either piece is already inserted and there are no more pairs on the far cell, go down to step 6 and use the algorithm to take the piece out of the slot.</li><br />
<li>Orient the pieces so that the same colours are on the far cell. Sune and antisune is used. Setup moves and RKT are a must.</li><br />
<li>Join the pair together using RKT moves. Twist the far cell until the pair is aligned as shown below (i.e. the green-orange-white pair on the D cell):<br><br />
[[File:C4a.png|400px]]<br><br />
It is possible for the pair to be oriented in two other ways. Make sure that the side colours of the S2L pair match the colours of the faces. Notice how the green and orange stickers match up with the side.<br />
<li>Now, the piece can be inserted using RKT. In this case, it is in the form of RU and D- instead of RK and T-, since you are treating the D cell as a 3^3. In the example shown above, since it is to the left of the slot from that viewpoint, it can be inserted using: (LU DT LU' DT') (LU' DT LU DT'). The next image shows the pair in place.<br><br />
[[File:C4b.png|400px]]</li><br />
<li>Repeat 7 more times.</li><br />
<li>Here is what it should look like when you are done (By now you should have used at most 450 moves):<br><br />
[[File:C4c.png|400px]]</li><br />
</ol><br />
<br />
====OLL====<br />
<ol><br />
<li>Use -U variants of OLL algorithms to orient the 2C pieces. (e.g. for line, FU RU TU RU' TU' FU')<br><br />
Attempt to orient as many 3C pieces in this step as possible.</li><br />
<li>For any unoriented 3C pieces, orient them using -U variants of corner OLL algorithms such as the sune.<br><br />
Note: if there is only one 3c piece left unoriented (see image below), place it so that it's facing you (see f2l flipped pair pic for reference). <br><br />
Use this algorithm if the piece needs to rotate CW: [RK2 RU' TR2 TU' LT2 LU' TR2 TU']*2. For rotating the other way, just reverse the algorithm.<br><br />
[[File:C5a.png|400px]]</li><br />
<br><br />
<li>Before starting to orient the 4C pieces, rotate the cube so that the up cell is now the far cell (T->U). The next image shows the transformation. (Notice the unoriented 3C piece. That is an error; orient all 3C pieces first!)<br><br />
[[File:C5b.png|400px]]</li><br />
<li>Do U- moves so that the unoriented 4C pieces have their U cell sticker (i.e. grey sticker) NOT on the T cell.</li> <br />
<li>Use RKT variants of corner OLL algorithms to orient the 4C piece. If by the end of the algorithm the right cell isn't aligned with the rest of the puzzle, do TF, turn RK until the right slice realigns, then do TF'. Repeat this step and the previous one until all 4C pieces are oriented.</li><br />
<li>If there is only one 4C piece left unoriented (see image below), place it so that it's facing you (see f2l flipped pair pic for reference). <br><br />
[[File:C5d.png|400px]]<br><br />
Then, do BR', use the RKT variant of the monoflip, and do BR. The monoflip to rotate the U-layer sticker of the FULT piece from the L cell to the U cell is as shown: [R U R' U']*2 L' [U R U' R']*2 L. Do the inverse for the algorithm that rotates the U-layer sticker of the FULT piece from the F cell to the U cell.<br />
</li><br />
<li>When all LL layer pieces have been oriented, the T cell should be one uniform colour. Rotate the puzzle back (U->T). The image below shows the unrotated puzzle.<br />
[[File:C5e.png|400px]]<br />
</li><br />
</ol><br />
<br />
====PLL====<br />
<ol><br />
<li>Do T- moves to match as many 2C pieces as possible (At least 2). Then use the -U variant of the U perms to match the rest. (See the first step of OLL for an example of a -U variant.)<br><br />
[[File:C6a.png|400px]]</li><br />
</li><br />
<li>From here, you use RKT moves to solve the rest of the puzzle like a 3^3. Parity: If the "top face" of the LL is 180 degrees off from the rest of the puzzle, use the RKT variant of the 180-degree-CW supercube center algorithm (R U R' U five times, OR L R U2 R' L' U twice).</li><br />
</ol><br/><br />
Please note that this step is very inefficient and can take up to 200 moves on its own.<br />
==Charles Doanâ€™s Method==<br />
This method consists of blockbuilding, as well as techniques from Roice Nelsonâ€™s method to solve the last few pieces. The method was intended for a low move count, as well as simply to serve as a unique method to solve the 4 dimensional Rubikâ€™s Cube. Using this method as a beginner is strongly advised against. There will be complex concepts that will be very difficult to grasp, therefore it is advised that this method only be utilized by individuals who have relatively proficient experience for the 3^4 cube. This method will be making use of the notation established by Raymond Zhao.<br />
<br />
===Prerequisites===<br />
<ol><br />
<li> To know how to solve the 4D Rubikâ€™s Cube using Roice Nelsonâ€™s method.<br />
<li> To be proficient at blockbuilding on a normal Rubikâ€™s Cube.<br />
<li> To have adequate experience for the 4D Rubikâ€™s Cube.<br />
</ol><br />
===Steps===<br />
<ol><br />
<li> Solve a 2*2*2*2 cube.<br />
<li> Expand the block to a 2*2*3*2.<br />
<li> Create a full or semi-F2L on the inner face.<br />
<li> Solve the First 2 Layers with or without missing 4-coloreds.<br />
<li> Solve the remaining pieces using Roice Nelsonâ€™s piece-by-piece method or Raymond Zhaoâ€™s OLL/PLL approach.<br />
</ol><br />
<br />
==Octachoroux Method==<br />
This method is Rowan Fortier's 4 dimensional equivalent of the Roux method. It aims for a more intuitive blockbuilding approach, and requires fewer algorithms that need to be memorized. The name Octachoroux comes from the word octachoron (which is another word for tesseract) and Roux.<br />
<br />
===Prerequisites===<br />
<ul><br />
<li> Knowledge of how the puzzle turns, and Zhao Notation </li><br />
<li> Knowledge of blockbuilding and the Roux method on the 3^3 </li><br />
<li> Knowledge of names of 4d pieces and the concept of RKT </li><br />
</ul><br />
<br />
===Summary of the Method:===<br />
<ul><br />
<li> First Block: Solve a 1x2x3x3 block using blockbuilding techniques </li><br />
<li> Second Block: Solve a 1x2x3x3 on the other side of the puzzle to complete your First 2 Blocks </li><br />
<li> CMLC: Orient and permute the corners of the U cell </li><br />
<li> L/R: Solve the Left and Right cells </li><br />
<li> M Slice: Permute the M slice </li><br />
</ul><br />
<br />
===First Block===<br />
Pick the colour of which first block you will be starting with. If you normally start with White or Yellow on D and any colour on the side, that would make you x2yw colour neutral. <br><br />
Build a 1x2x3x3 block. You could solve the 2c pieces first, and then use the K cell to easily pair up pieces without disturbing your progress on the T cell. Then you can just bring those pairs onto the T cell and insert them using -K moves as normal 3^3 twists. <br><br />
Once this step is completed, hold the first block on the left, just as in normal Roux. <br><br />
[[File:Firstblock_2.png|400px]] [[File:Firstblock_1.png|400px]]<br />
<br />
===Second Block===<br />
Make the same 1x2x3x3 block, just on the other side. Start with the DR 2c piece. After that you can solve the other 4 2c pieces by bringing them to TU and doing RF TF' RF' to insert them. You can use many of the same tricks from the 3^3, such as hiding an edge in TDF and then rotating the U cell to bring the corner the edge pairs up with onto the T cell, then connecting them with M moves. RKT is necessary to insert pairs without messing up the first block. <br><br />
[[File:Secondblock.png|400px]]<br />
<br />
===CMLC (CO)===<br />
Bring the U cell to T, then use RKT to set up a layer so that it looks like a normal OCLL case, then bring the T cell to U. Hold that case so that it is in the D layer of the U cell, as shown in the image below, and use RKT variants of OCLL algorithms to orient those pieces. <br><br />
[[File:CMLC_CO1.png|400px]] <br><br />
Repeat this until all the corners are oriented. If you just have 1 corner left to twist, a good intuitive way to do this is to untwist 2 other corners, then use RKT to set that up in to a Sune case. You can also use the Monoflip algorithm described in the Sheerin-Zhao method above. <br><br />
[[File:CMLC_CO2.png||400px]]<br />
<br />
===CMLC (CP)===<br />
Now bring the U cell to T and use RKT to permute it like a regular 2x2x2 Rubik's cube. If you get a parity where a layer ends up being off by 180 degrees, use the RKT parity algorithm: <br><br />
TU UR T[LFU]' UK' TF RF UR RF' U[TR] <br><br />
It will look like this when it is done. Rotate the T cell back to the U cell <br><br />
[[File:CMLC_CP2.png|400px]]<br />
<br />
===L/R===<br />
Instead of orienting the edges like in 3^3 Roux, just go directly to solving the Left and Right cells of the cube. The reason why will become apparent later. <br><br />
First solve the 2c pieces with the L/R and U colour. <br><br />
Now you setup edges that need to go to L/R into the TDF spot with the L/R colour on the T cell and the U colour on the D cell. Then move the spot where that L/R edge needs to go above that edge and insert that piece using the RKT algorithm of M D2 M' D2 (2RK' TF' RK2 TF 2RK TF' RK2 TF) <br><br />
[[File:LR2.png|400px]] <br><br />
There are 8 edges total that need to be inserted for L/R do be complete.<br />
<br />
===M slice===<br />
[[File:M1.png|400px]] <br><br />
Now all you have to do is permute the M slice. This step is pretty similar to PLL from Sheerin-Zhao method, but with some key differences. <br><br />
<ul><br />
<li> Pieces have the same number of colours as they do on the 3^3. Corners pieces have 3, edges have 2, etc. </li><br />
<li> Pieces can look "mirrored" </li><br />
<li> There is no RKT parity </li><br />
</ul><br />
Now you can either use UR moves as U, U', U2 moves, and M slice rotations to do RKT (called URM), or rotate to bring one of the L/R sides to the T cell and use normal RKT, except you have to hold down 2 on your keyboard in order to do T moves. <br><br />
There are some interesting "parities" you might encounter that are impossible on both the 3^3, and the 3^3 last layer of CFOP 3^4. Such as: <br><br />
<ul><br />
<li> Corner pieces that look "mirrored" </li><br />
<li> Impossible Last Layer/CMLL(/whatever method you use) cases </li><br />
</ul><br />
If you solve the M slice using CFOP, then once you get to PLL, you can rotate the puzzle so that the U cell goes to T, and then orient the edges onto the T cell and then permute that like step 4c of the Roux method. <br><br />
If you solve the M slice using Roux, then look forward to impossible CO and CP cases from 2-look CMLL. <br><br />
An algorithm that is super useful here is a pure 2-flip of 3c pieces. I use M' U M' U M' U M' U2 M' U M' U M' U M' using RKT.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=3%5E4&diff=33863^42021-08-27T04:32:10Z<p>Blobinati: </p>
<hr />
<div>Visit [http://wiki.superliminal.com/wiki/Notation this page] to get an overview of the different notation systems to describe moves on the 3^4. <br><br />
<br />
==Roice's Method==<br />
Roice's Method is a piece-by-piece solution that uses commutators that successively build on each other to solve one type of piece at a time.<br />
A link to the method can be found here.<br />
[http://www.superliminal.com/cube/solution/solution.htm Ultimate Solution to a 3x3x3x3.] <br><br />
<br />
Additionally, Charles Doan has developed a system to implement this method. The tutorials can be found [https://m.youtube.com/playlist?list=PLt_EqFtx5iHwBkNDgqpdX8oVoRuUJejzR here.]<br />
<br />
<br>Below is notation used by Ray Zhao.<br />
<br />
===RKT===<br />
RKT is a technique that is used to execute moves that damage fewer pieces. By using RKT, the solver picks a cell that the solver wants to treat i.e. as a 3^3 (If it was a 4^4 you were solving, RKT would treat a cell as a 4^3). The main idea is to only use RK and T- moves.<br> <br />
For example,<br><br />
<ol><br />
<li>On a 3^3, you can do the sune algorithm: R U R' U R U2 R'. This is an OLL algorithm that can be used to orient corners, but is also able to permute edges (while breaking corners).<br />
</li><br />
<li>On a 3^4, if you replace the algorithm above like so: R=RU, U=TU, you can see that the algorithm seems to have moved 3x1x1x1 blocks. That means that 2c, 3c and 4c are all moved. What if you only want to affect the 3c and 4c of the top 3x3x1x1 block of the T cell? (aka the TU ridge)<br />
</li><br />
<li>Well, back on the 3^3, you can execute sune by doing only R turns and cube rotations. This becomes R z R z' R' z R z' R z R2 z' R'. Notice that the z turn brings the U face into the position of the R face, and the z' turn brings back the original R face.<br />
</li><br />
<li>Now to convert the 3^3 algorithm from the previous step into an RKT algorithm, just substitute R=RK and z=TF. Notice how the T cell seems to be affected in the exact same way the 3^3 was affected in the last step; treating the T cell as a 3^3, it seems to undergo z and R turns. <br />
</li><br />
</ol><br><br />
Note that even though this method is called RKT, it is not limited to those types of turns. Thus, you can use LK and T- moves instead, or rotate your view and use RU and D- instead of RK and T-!<br />
<br />
==Sheerin-Zhao Method (Hybrid) V1==<br />
This method is an attempt to make a 4D analogue of the Fridrich/CFOP method. Using this method results in around 650 to 900 moves, even if no shortcut turns are used. This method needs significant improvement because of the move count required for the last layer. <br />
<br />
===Prerequisites===<br />
<ul><br />
<li>Knowledge of how the cube rotates.</li><br />
<li>The Fridrich Method (F2L/OLL/PLL). 2-look OLL/PLL is enough.</li><br />
<li>Some commutators, especially the monoflip. (R' D' R D R' D R and its inverse)</li><br />
<li>The notation described above</li><br />
</ul><br />
===Summary of the Method===<br />
<ol><br />
<li>Cross: Make a cross by solving 8 2C pieces on the far cell.</li><br />
<li>F2L: Fill in F2L slots by joining F2L pairs (2C/3C) together and inserting them into their respective slots.</li><br />
<li>S2L: Fill in S2L slots. This is done by moving a 3C piece and its respective 4C piece onto the farthest cell. Then, OLL algorithms are used to orient the pieces so that they can be joined using RKT moves. They are then inserted using modified RKT moves.</li><br />
<li>OLL: Orient the LL 2C pieces, 3C pieces, ''then'' the 4C pieces using OLL-C (corner OLL) algorithms, such as the sune/antisune. Try to get as many corners oriented as possible as well. Setup moves are highly recommended here.</li><br />
<li>Pre-PLL: Permute the 2C of the LL using U-perms. </li><br />
<li>PLL: Solve the LL like a 3^3 by using RKT moves. (The cube is rotated at this stage)</li><br />
<li>Parity: If the "top face" of the LL is 180 degrees off from the rest of the puzzle, use the RKT variant of the 180-degree-CW supercube center algorithm (R U R' U five times, OR L R U2 R' L' U twice).</li><br />
</ol><br />
<br />
===Method===<br />
====Cross====<br />
<ol><br />
<li>Pick the colour that you will be using for the near cell (the cell not inside the viewpoint). In this example, cyan is chosen.</li><br />
<li>Rotate the puzzle so that the cell with that specified colour is now the near cell.</li><br />
<li>Intuitively place all -K (2C face) pieces oriented and permuted correctly.<br><br />
This image shows the solved cross.<br />
<br>[[File:C2.png|400px]]<br />
</li><br />
</ol><br />
<br />
====F2L====<br />
<ol><br />
<li>Find any 2C piece that does not include a sticker with the colour of the far cell (i.e. grey).</li><br />
<li>Find the 3C piece with the stickers that have the same colours of the 2C piece and of the near cell. For example, if the 2C piece's colours were red and yellow and the near cell piece was cyan, the 3C piece would be red, yellow, and cyan.</li><br />
<li>Intuitively align the two pieces so that they lie on the same slice on the far cell.</li><br />
<li>Join the pair together and insert the pair into the slot using -U moves.</li><br />
<li>Repeat 11 more times. <br>Note: It is possible to insert the slot flipped. There are many shortcuts in forming pairs too. The image below shows the flipped pair (white-blue).<br />
<br>[[File:C3a.png|400px]]<br />
</li><br />
<li>Here is what it should look like when you are done:<br />
<br>[[File:C3b.png|400px]]</li><br />
</ol><br />
<br />
====S2L====<br />
<ol><br />
<li>Find any 3C piece that does not include a sticker with the colour of the far cell (i.e. grey).</li><br />
<li>Find its respective 4C piece (see F2L for details).<br><br />
note: try finding pairs that are already on the far cell first.</li><br />
<li>If either piece is already inserted and there are no more pairs on the far cell, go down to step 6 and use the algorithm to take the piece out of the slot.</li><br />
<li>Orient the pieces so that the same colours are on the far cell. Sune and antisune is used. Setup moves and RKT are a must.</li><br />
<li>Join the pair together using RKT moves. Twist the far cell until the pair is aligned as shown below (i.e. the green-orange-white pair on the D cell):<br><br />
[[File:C4a.png|400px]]<br><br />
It is possible for the pair to be oriented in two other ways. Make sure that the side colours of the S2L pair match the colours of the faces. Notice how the green and orange stickers match up with the side.<br />
<li>Now, the piece can be inserted using RKT. In this case, it is in the form of RU and D- instead of RK and T-, since you are treating the D cell as a 3^3. In the example shown above, since it is to the left of the slot from that viewpoint, it can be inserted using: (LU DT LU' DT') (LU' DT LU DT'). The next image shows the pair in place.<br><br />
[[File:C4b.png|400px]]</li><br />
<li>Repeat 7 more times.</li><br />
<li>Here is what it should look like when you are done (By now you should have used at most 450 moves):<br><br />
[[File:C4c.png|400px]]</li><br />
</ol><br />
<br />
====OLL====<br />
<ol><br />
<li>Use -U variants of OLL algorithms to orient the 2C pieces. (e.g. for line, FU RU TU RU' TU' FU')<br><br />
Attempt to orient as many 3C pieces in this step as possible.</li><br />
<li>For any unoriented 3C pieces, orient them using -U variants of corner OLL algorithms such as the sune.<br><br />
Note: if there is only one 3c piece left unoriented (see image below), place it so that it's facing you (see f2l flipped pair pic for reference). <br><br />
Use this algorithm if the piece needs to rotate CW: [RK2 RU' TR2 TU' LT2 LU' TR2 TU']*2. For rotating the other way, just reverse the algorithm.<br><br />
[[File:C5a.png|400px]]</li><br />
<br><br />
<li>Before starting to orient the 4C pieces, rotate the cube so that the up cell is now the far cell (T->U). The next image shows the transformation. (Notice the unoriented 3C piece. That is an error; orient all 3C pieces first!)<br><br />
[[File:C5b.png|400px]]</li><br />
<li>Do U- moves so that the unoriented 4C pieces have their U cell sticker (i.e. grey sticker) NOT on the T cell.</li> <br />
<li>Use RKT variants of corner OLL algorithms to orient the 4C piece. If by the end of the algorithm the right cell isn't aligned with the rest of the puzzle, do TF, turn RK until the right slice realigns, then do TF'. Repeat this step and the previous one until all 4C pieces are oriented.</li><br />
<li>If there is only one 4C piece left unoriented (see image below), place it so that it's facing you (see f2l flipped pair pic for reference). <br><br />
[[File:C5d.png|400px]]<br><br />
Then, do BR', use the RKT variant of the monoflip, and do BR. The monoflip to rotate the U-layer sticker of the FULT piece from the L cell to the U cell is as shown: [R U R' U']*2 L' [U R U' R']*2 L. Do the inverse for the algorithm that rotates the U-layer sticker of the FULT piece from the F cell to the U cell.<br />
</li><br />
<li>When all LL layer pieces have been oriented, the T cell should be one uniform colour. Rotate the puzzle back (U->T). The image below shows the unrotated puzzle.<br />
[[File:C5e.png|400px]]<br />
</li><br />
</ol><br />
<br />
====PLL====<br />
<ol><br />
<li>Do T- moves to match as many 2C pieces as possible (At least 2). Then use the -U variant of the U perms to match the rest. (See the first step of OLL for an example of a -U variant.)<br><br />
[[File:C6a.png|400px]]</li><br />
</li><br />
<li>From here, you use RKT moves to solve the rest of the puzzle like a 3^3. Parity: If the "top face" of the LL is 180 degrees off from the rest of the puzzle, use the RKT variant of the 180-degree-CW supercube center algorithm (R U R' U five times, OR L R U2 R' L' U twice).</li><br />
</ol><br/><br />
Please note that this step is very inefficient and can take up to 200 moves on its own.<br />
==Charles Doanâ€™s Method==<br />
This method consists of blockbuilding, as well as techniques from Roice Nelsonâ€™s method to solve the last few pieces. The method was intended for a low move count, as well as simply to serve as a unique method to solve the 4 dimensional Rubikâ€™s Cube. Using this method as a beginner is strongly advised against. There will be complex concepts that will be very difficult to grasp, therefore it is advised that this method only be utilized by individuals who have relatively proficient experience for the 3^4 cube. This method will be making use of the notation established by Raymond Zhao.<br />
<br />
===Prerequisites===<br />
<ol><br />
<li> To know how to solve the 4D Rubikâ€™s Cube using Roice Nelsonâ€™s method.<br />
<li> To be proficient at blockbuilding on a normal Rubikâ€™s Cube.<br />
<li> To have adequate experience for the 4D Rubikâ€™s Cube.<br />
</ol><br />
===Steps===<br />
<ol><br />
<li> Solve a 2*2*2*2 cube.<br />
<li> Expand the block to a 2*2*3*2.<br />
<li> Create a full or semi-F2L on the inner face.<br />
<li> Solve the First 2 Layers with or without missing 4-coloreds.<br />
<li> Solve the remaining pieces using Roice Nelsonâ€™s piece-by-piece method or Raymond Zhaoâ€™s OLL/PLL approach.<br />
</ol><br />
<br />
==Octachoroux Method==<br />
This method is Rowan Fortier's 4 dimensional equivalent of the Roux method. It aims for a more intuitive blockbuilding approach, and requires fewer algorithms that need to be memorized. The name Octachoroux comes from the word octachoron (which is another word for tesseract) and Roux.<br />
<br />
===Prerequisites===<br />
<ul><br />
<li> Knowledge of how the puzzle turns, and Zhao Notation </li><br />
<li> Knowledge of blockbuilding and the Roux method on the 3^3 </li><br />
<li> Knowledge of names of 4d pieces and the concept of RKT </li><br />
</ul><br />
<br />
===Summary of the Method:===<br />
<ul><br />
<li> First Block: Solve a 1x2x3x3 block using blockbuilding techniques </li><br />
<li> Second Block: Solve a 1x2x3x3 on the other side of the puzzle to complete your First 2 Blocks </li><br />
<li> CMLC: Orient and permute the corners of the U cell </li><br />
<li> L/R: Solve the Left and Right cells </li><br />
<li> M Slice: Permute the M slice </li><br />
</ul><br />
<br />
===First Block===<br />
Pick the colour of which first block you will be starting with. If you normally start with White or Yellow on D and any colour on the side, that would make you x2yw colour neutral. <br><br />
Build a 1x2x3x3 block. You could solve the 2c pieces first, and then use the K cell to easily pair up pieces without disturbing your progress on the T cell. Then you can just bring those pairs onto the T cell and insert them using -K moves as normal 3^3 twists. <br><br />
Once this step is completed, hold the first block on the left, just as in normal Roux. <br><br />
[[File:Firstblock_2.png|400px]] [[File:Firstblock_1.png|400px]]<br />
<br />
===Second Block===<br />
Make the same 1x2x3x3 block, just on the other side. Start with the DR 2c piece. After that you can solve the other 4 2c pieces by bringing them to TU and doing RF TF' RF' to insert them. You can use many of the same tricks from the 3^3, such as hiding an edge in TDF and then rotating the U cell to bring the corner the edge pairs up with onto the T cell, then connecting them with M moves. RKT is necessary to insert pairs without messing up the first block. <br><br />
[[File:Secondblock.png|400px]]<br />
<br />
===CMLC (CO)===<br />
Bring the U cell to T, then use RKT to set up a layer so that it looks like a normal OCLL case, then bring the T cell to U. Hold that case so that it is in the D layer of the U cell, as shown in the image below, and use RKT variants of OCLL algorithms to orient those pieces. <br><br />
[[File:CMLC_CO1.png|400px]] <br><br />
Repeat this until all the corners are oriented. If you just have 1 corner left to twist, a good intuitive way to do this is to untwist 2 other corners, then use RKT to set that up in to a Sune case. You can also use the Monoflip algorithm described in the Sheerin-Zhao method above. <br><br />
[[File:CMLC_CO2.png||400px]]<br />
<br />
===CMLC (CP)===<br />
Now bring the U cell to T and use RKT to permute it like a regular 2x2x2 Rubik's cube. If you get a parity where a layer ends up being off by 180 degrees, use the RKT parity algorithm: <br><br />
TU UR T[LFU]' UK' TF RF UR RF' U[TR] <br><br />
It will look like this when it is done. Rotate the T cell back to the U cell <br><br />
[[File:CMLC_CP2.png|400px]]<br />
<br />
===L/R===<br />
Instead of orienting the edges like in 3^3 Roux, just go directly to solving the Left and Right cells of the cube. The reason why will become apparent later. <br><br />
First solve the 2c pieces with the L/R and U colour. <br><br />
Now you setup edges that need to go to L/R into the TDF spot with the L/R colour on the T cell and the U colour on the D cell. Then move the spot where that L/R edge needs to go above that edge and insert that piece using the RKT algorithm of M D2 M' D2 (2RK' TF' RK2 TF 2RK TF' RK2 TF) <br><br />
[[File:LR2.png|400px]] <br><br />
There are 8 edges total that need to be inserted for L/R do be complete.<br />
<br />
===M slice===<br />
[[File:M1.png|400px]] <br><br />
Now all you have to do is permute the M slice. This step is pretty similar to PLL from Sheerin-Zhao method, but with some key differences. <br><br />
<ul><br />
<li> Pieces have the same number of colours as they do on the 3^3. Corners pieces have 3, edges have 2, etc. </li><br />
<li> Pieces can look "mirrored" </li><br />
<li> There is no RKT parity </li><br />
</ul><br />
Now you can either use UR moves as U, U', U2 moves, and M slice rotations to do RKT (called URM), or rotate to bring one of the L/R sides to the T cell and use normal RKT, except you have to hold down 2 on your keyboard in order to do T moves. <br><br />
There are some interesting "parities" you might encounter that are impossible on both the 3^3, and the 3^3 last layer of CFOP 3^4. Such as: <br><br />
<ul><br />
<li> Corner pieces that look "mirrored" </li><br />
<li> Impossible Last Layer/CMLL(/whatever method you use) cases </li><br />
</ul><br />
If you solve the M slice using CFOP, then once you get to PLL, you can rotate the puzzle so that the U cell goes to T, and then orient the edges onto the T cell and then permute that like step 4c of the Roux method. <br><br />
If you solve the M slice using Roux, then look forward to impossible CO and CP cases from 2-look CMLL. <br><br />
An algorithm that is super useful here is a pure 2-flip of 3c pieces. I use M' U M' U M' U M' U2 M' U M' U M' U M' using RKT.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=Notation&diff=3385Notation2021-08-27T04:29:10Z<p>Blobinati: </p>
<hr />
<div>==n^4:==<br />
===Commonly Used Notations:===<br />
<br />
'''Zhao Notation:''' <br><br />
The notation is similar to that of the 3^3. There are 8 cells, six of them using the same letters as that in the 3^3: U (up), D (down), F (front), B (back), R (right), L (left). The near cell which is not visible, is named K, for kata. The far cell, which appears as the innermost cell, is named T, for top. (''Thanks to Neodam22 for pointing out the problem!'') Its name was changed from A to T since ana and kata are easier to confuse with each other than kata and "top".<br><br />
Each cell in turn uses [http://worldcubeassociation.org/regulations/#notation WCA Official Notation] (standard notation).<br><br />
'''The first letter determines the cell to click on. The second letter determines the sticker on the cell (is usually a 2C piece) to click on''' For example: <br><br />
RK means to click the sticker on the right cell that joins to the near cell.<br><br />
TF means to click the sticker on the far cell that joins to the front cell.<br><br />
FT means to click the sticker on the front cell that joins to the far cell.<br><br />
To state a set of all possible turns (clicks) of a cell, X- is used. For example: R- includes RU, RF, RD, RB, RT, and RK.<br><br />
To state a set of all possible turns (clicks) of cells that are joined to the original sticker to be clicked, -X is used. For example, -R includes UR, FR, DR and BR, TR and KR. <br><br />
Slice and wide turns can be notated with the 2c piece that you click on, plus the number you hold down to perform that move. For example, 2RK is like an M', and 12RK is like Rw'. <br><br />
<br />
'''I/O variant of Zhao Notation''' <br> <br />
Some people in the community prefer to use I (Inner) instead of T, and O (Outer) instead of K. <br> <br />
This makes it more obvious which face is which, whereas "Top" can be confused with Up <br><br />
<br />
'''Rotation Notation:'''<br><br />
Rotation Notation uses the same cell names from Zhao's Notation, but uses 3^3 x, y, and z rotations to be more intuitive. <br><br />
Each turn is made up of the face you click in followed by which rotation that face undergoes. <br><br />
If you wanted to make the F face of the T cell become the U face of the T cell, that would be Tx because it's rotating the T cell clockwise along the x axis. <br><br />
One of the downsides of this notation is that edge and corner twist moves become longer. For example: T[UF] becomes Tz2x. <br><br />
<br />
===Experimental Notations:===<br />
<br />
'''Blob Notation:''' <br><br />
Blob Notation was an attempt by Blobinati Cuber to make Zhao Notation more efficient by making each of the 13 symmetries of a cube into a letter (a-m) following the main 8 letters that represent the cells. <br> <br />
a, b, & c were y, x, & z rotations, and the rest were various corner and edge twists. <br><br />
This notation does succeed in making corner and edge twist moves take up less letters to write, at the cost of having to memorize 13 new letters and what their moves look like. <br><br />
<br />
'''Picture Notation''' <br><br />
Picture Notation was an attempt by Blobinati Cuber to make Zhao Notation easier to visualize by using little pictures to represent the cells' rotations. If you imagine that you are looking into the inside of a box from one of the faces, then the possible shapes you can see is the small square, the big square, and the 4 trapezoids in-between, which are just squished squares due to the projection of the cube onto 2d space. <br><br />
You start each turn by imagining the letter that represents that cell (U, D, R, L, F, B, T, K) is on the F face. Then, perform the rotations of the cell and draw the letter on the correct shape and orientation to represent where it ended up.<br />
<br />
===Uncommon/old Notations:===<br />
<br />
'''Roice Notation:''' <br><br />
Roice's Notation uses different names for the cells. <br><br />
[[File:RoiceNotation.gif|400px]] <br><br />
Each cell's stickers are numbered from 1-27 like this: <br><br />
[[File:smallNumbers.png|400px]] <br><br />
You then state whether you did a right or left click. Examples: <br><br />
Top, 5, Left <br><br />
Left, 9, Right <br><br />
<br />
===Examples:===<br />
Below are examples of the 9 move RKT parity algorithm in all of the above notations. <br><br />
TU UR T[LFU]' UK' TF RF UR RF' U[TR] <br><br />
IU UR I[LFU]' UO' IF RF UR RF' U[IR] <br><br />
Ty Ux Tz'x Uy' Tz Rz Ux Rz' Ux2z <br></div>Blobinatihttp://wiki.superliminal.com/index.php?title=File:SmallNumbers.png&diff=3384File:SmallNumbers.png2021-08-27T04:28:46Z<p>Blobinati: </p>
<hr />
<div></div>Blobinatihttp://wiki.superliminal.com/index.php?title=Notation&diff=3383Notation2021-08-27T04:25:49Z<p>Blobinati: </p>
<hr />
<div>==n^4:==<br />
===Commonly Used Notations:===<br />
<br />
'''Zhao Notation:''' <br><br />
The notation is similar to that of the 3^3. There are 8 cells, six of them using the same letters as that in the 3^3: U (up), D (down), F (front), B (back), R (right), L (left). The near cell which is not visible, is named K, for kata. The far cell, which appears as the innermost cell, is named T, for top. (''Thanks to Neodam22 for pointing out the problem!'') Its name was changed from A to T since ana and kata are easier to confuse with each other than kata and "top".<br><br />
Each cell in turn uses [http://worldcubeassociation.org/regulations/#notation WCA Official Notation] (standard notation).<br><br />
'''The first letter determines the cell to click on. The second letter determines the sticker on the cell (is usually a 2C piece) to click on''' For example: <br><br />
RK means to click the sticker on the right cell that joins to the near cell.<br><br />
TF means to click the sticker on the far cell that joins to the front cell.<br><br />
FT means to click the sticker on the front cell that joins to the far cell.<br><br />
To state a set of all possible turns (clicks) of a cell, X- is used. For example: R- includes RU, RF, RD, RB, RT, and RK.<br><br />
To state a set of all possible turns (clicks) of cells that are joined to the original sticker to be clicked, -X is used. For example, -R includes UR, FR, DR and BR, TR and KR. <br><br />
Slice and wide turns can be notated with the 2c piece that you click on, plus the number you hold down to perform that move. For example, 2RK is like an M', and 12RK is like Rw'. <br><br />
<br />
'''I/O variant of Zhao Notation''' <br> <br />
Some people in the community prefer to use I (Inner) instead of T, and O (Outer) instead of K. <br> <br />
This makes it more obvious which face is which, whereas "Top" can be confused with Up <br><br />
<br />
'''Rotation Notation:'''<br><br />
Rotation Notation uses the same cell names from Zhao's Notation, but uses 3^3 x, y, and z rotations to be more intuitive. <br><br />
Each turn is made up of the face you click in followed by which rotation that face undergoes. <br><br />
If you wanted to make the F face of the T cell become the U face of the T cell, that would be Tx because it's rotating the T cell clockwise along the x axis. <br><br />
One of the downsides of this notation is that edge and corner twist moves become longer. For example: T[UF] becomes Tz2x. <br><br />
<br />
===Experimental Notations:===<br />
<br />
'''Blob Notation:''' <br><br />
Blob Notation was an attempt by Blobinati Cuber to make Zhao Notation more efficient by making each of the 13 symmetries of a cube into a letter (a-m) following the main 8 letters that represent the cells. <br> <br />
a, b, & c were y, x, & z rotations, and the rest were various corner and edge twists. <br><br />
This notation does succeed in making corner and edge twist moves take up less letters to write, at the cost of having to memorize 13 new letters and what their moves look like. <br><br />
<br />
'''Picture Notation''' <br><br />
Picture Notation was an attempt by Blobinati Cuber to make Zhao Notation easier to visualize by using little pictures to represent the cells' rotations. If you imagine that you are looking into the inside of a box from one of the faces, then the possible shapes you can see is the small square, the big square, and the 4 trapezoids in-between, which are just squished squares due to the projection of the cube onto 2d space. <br><br />
You start each turn by imagining the letter that represents that cell (U, D, R, L, F, B, T, K) is on the F face. Then, perform the rotations of the cell and draw the letter on the correct shape and orientation to represent where it ended up.<br />
<br />
===Uncommon/old Notations:===<br />
<br />
'''Roice Notation:''' <br><br />
Roice's Notation uses different names for the cells. <br><br />
[[File:RoiceNotation.gif|400px]] <br><br />
Each cell's stickers are numbered from 1-27 like this: <br><br />
[[File:RoiceNumbered.gif|400px]] <br><br />
You then state whether you did a right or left click. Examples: <br><br />
Top, 5, Left <br><br />
Left, 9, Right <br><br />
<br />
===Examples:===<br />
Below are examples of the 9 move RKT parity algorithm in all of the above notations. <br><br />
TU UR T[LFU]' UK' TF RF UR RF' U[TR] <br><br />
IU UR I[LFU]' UO' IF RF UR RF' U[IR] <br><br />
Ty Ux Tz'x Uy' Tz Rz Ux Rz' Ux2z <br></div>Blobinatihttp://wiki.superliminal.com/index.php?title=File:RoiceNumbered.gif&diff=3382File:RoiceNumbered.gif2021-08-27T04:08:03Z<p>Blobinati: </p>
<hr />
<div></div>Blobinatihttp://wiki.superliminal.com/index.php?title=Notation&diff=3381Notation2021-08-27T04:07:46Z<p>Blobinati: </p>
<hr />
<div>==n^4:==<br />
===Commonly Used Notations:===<br />
<br />
'''Zhao Notation:''' <br><br />
The notation is similar to that of the 3^3. There are 8 cells, six of them using the same letters as that in the 3^3: U (up), D (down), F (front), B (back), R (right), L (left). The near cell which is not visible, is named K, for kata. The far cell, which appears as the innermost cell, is named T, for top. (''Thanks to Neodam22 for pointing out the problem!'') Its name was changed from A to T since ana and kata are easier to confuse with each other than kata and "top".<br><br />
Each cell in turn uses [http://worldcubeassociation.org/regulations/#notation WCA Official Notation] (standard notation).<br><br />
'''The first letter determines the cell to click on. The second letter determines the sticker on the cell (is usually a 2C piece) to click on''' For example: <br><br />
RK means to click the sticker on the right cell that joins to the near cell.<br><br />
TF means to click the sticker on the far cell that joins to the front cell.<br><br />
FT means to click the sticker on the front cell that joins to the far cell.<br><br />
To state a set of all possible turns (clicks) of a cell, X- is used. For example: R- includes RU, RF, RD, RB, RT, and RK.<br><br />
To state a set of all possible turns (clicks) of cells that are joined to the original sticker to be clicked, -X is used. For example, -R includes UR, FR, DR and BR, TR and KR. <br><br />
Slice and wide turns can be notated with the 2c piece that you click on, plus the number you hold down to perform that move. For example, 2RK is like an M', and 12RK is like Rw'. <br><br />
<br />
'''I/O variant of Zhao Notation''' <br> <br />
Some people in the community prefer to use I (Inner) instead of T, and O (Outer) instead of K. <br> <br />
This makes it more obvious which face is which, whereas "Top" can be confused with Up <br><br />
<br />
'''Rotation Notation:'''<br><br />
Rotation Notation uses the same cell names from Zhao's Notation, but uses 3^3 x, y, and z rotations to be more intuitive. <br><br />
Each turn is made up of the face you click in followed by which rotation that face undergoes. <br><br />
If you wanted to make the F face of the T cell become the U face of the T cell, that would be Tx because it's rotating the T cell clockwise along the x axis. <br><br />
One of the downsides of this notation is that edge and corner twist moves become longer. For example: T[UF] becomes Tz2x. <br><br />
<br />
===Experimental Notations:===<br />
<br />
'''Blob Notation:''' <br><br />
Blob Notation was an attempt by Blobinati Cuber to make Zhao Notation more efficient by making each of the 13 symmetries of a cube into a letter (a-m) following the main 8 letters that represent the cells. <br> <br />
a, b, & c were y, x, & z rotations, and the rest were various corner and edge twists. <br><br />
This notation does succeed in making corner and edge twist moves take up less letters to write, at the cost of having to memorize 13 new letters and what their moves look like. <br><br />
<br />
'''Picture Notation'''<br />
<br />
===Uncommon/old Notations:===<br />
<br />
'''Roice Notation:''' <br><br />
Roice's Notation uses different names for the cells. <br><br />
[[File:RoiceNotation.gif|400px]] <br><br />
Each cell's stickers are numbered from 1-27 on the 3^3, and after that you state whether you performed a left or right click. <br></div>Blobinatihttp://wiki.superliminal.com/index.php?title=Notation&diff=3380Notation2021-08-27T03:56:16Z<p>Blobinati: /* Uncommon/old Notations: */</p>
<hr />
<div>==n^4:==<br />
===Commonly Used Notations:===<br />
<br />
'''Zhao Notation:''' <br><br />
The notation is similar to that of the 3^3. There are 8 cells, six of them using the same letters as that in the 3^3: U (up), D (down), F (front), B (back), R (right), L (left). The near cell which is not visible, is named K, for kata. The far cell, which appears as the innermost cell, is named T, for top. (''Thanks to Neodam22 for pointing out the problem!'') Its name was changed from A to T since ana and kata are easier to confuse with each other than kata and "top".<br><br />
Each cell in turn uses [http://worldcubeassociation.org/regulations/#notation WCA Official Notation] (standard notation).<br><br />
'''The first letter determines the cell to click on. The second letter determines the sticker on the cell (is usually a 2C piece) to click on''' For example: <br><br />
RK means to click the sticker on the right cell that joins to the near cell.<br><br />
TF means to click the sticker on the far cell that joins to the front cell.<br><br />
FT means to click the sticker on the front cell that joins to the far cell.<br><br />
To state a set of all possible turns (clicks) of a cell, X- is used. For example: R- includes RU, RF, RD, RB, RT, and RK.<br><br />
To state a set of all possible turns (clicks) of cells that are joined to the original sticker to be clicked, -X is used. For example, -R includes UR, FR, DR and BR, TR and KR. <br><br />
Slice and wide turns can be notated with the 2c piece that you click on, plus the number you hold down to perform that move. For example, 2RK is like an M', and 12RK is like Rw'. <br><br />
<br />
'''I/O variant of Zhao Notation''' <br> <br />
Some people in the community prefer to use I (Inner) instead of T, and O (Outer) instead of K. <br> <br />
This makes it more obvious which face is which, whereas "Top" can be confused with Up <br><br />
<br />
'''Rotation Notation:'''<br><br />
Rotation Notation uses the same cell names from Zhao's Notation, but uses 3^3 x, y, and z rotations to be more intuitive. <br><br />
Each turn is made up of the face you click in followed by which rotation that face undergoes. <br><br />
If you wanted to make the F face of the T cell become the U face of the T cell, that would be Tx because it's rotating the T cell clockwise along the x axis. <br><br />
One of the downsides of this notation is that edge and corner twist moves become longer. For example: T[UF] becomes Tz2x. <br><br />
<br />
===Experimental Notations:===<br />
'''Blob Notation:'''<br />
<br><br />
'''<br />
<br />
===Uncommon/old Notations:===<br />
<br />
'''Roice Notation:''' <br><br />
Roice's Notation uses different names for the cells. <br><br />
[[File:RoiceNotation.gif|400px]] <br><br />
Each cell's stickers are numbered from 1-27 on the 3^3, and after that you state whether you performed a left or right click. <br></div>Blobinatihttp://wiki.superliminal.com/index.php?title=Notation&diff=3379Notation2021-08-27T03:56:06Z<p>Blobinati: </p>
<hr />
<div>==n^4:==<br />
===Commonly Used Notations:===<br />
<br />
'''Zhao Notation:''' <br><br />
The notation is similar to that of the 3^3. There are 8 cells, six of them using the same letters as that in the 3^3: U (up), D (down), F (front), B (back), R (right), L (left). The near cell which is not visible, is named K, for kata. The far cell, which appears as the innermost cell, is named T, for top. (''Thanks to Neodam22 for pointing out the problem!'') Its name was changed from A to T since ana and kata are easier to confuse with each other than kata and "top".<br><br />
Each cell in turn uses [http://worldcubeassociation.org/regulations/#notation WCA Official Notation] (standard notation).<br><br />
'''The first letter determines the cell to click on. The second letter determines the sticker on the cell (is usually a 2C piece) to click on''' For example: <br><br />
RK means to click the sticker on the right cell that joins to the near cell.<br><br />
TF means to click the sticker on the far cell that joins to the front cell.<br><br />
FT means to click the sticker on the front cell that joins to the far cell.<br><br />
To state a set of all possible turns (clicks) of a cell, X- is used. For example: R- includes RU, RF, RD, RB, RT, and RK.<br><br />
To state a set of all possible turns (clicks) of cells that are joined to the original sticker to be clicked, -X is used. For example, -R includes UR, FR, DR and BR, TR and KR. <br><br />
Slice and wide turns can be notated with the 2c piece that you click on, plus the number you hold down to perform that move. For example, 2RK is like an M', and 12RK is like Rw'. <br><br />
<br />
'''I/O variant of Zhao Notation''' <br> <br />
Some people in the community prefer to use I (Inner) instead of T, and O (Outer) instead of K. <br> <br />
This makes it more obvious which face is which, whereas "Top" can be confused with Up <br><br />
<br />
'''Rotation Notation:'''<br><br />
Rotation Notation uses the same cell names from Zhao's Notation, but uses 3^3 x, y, and z rotations to be more intuitive. <br><br />
Each turn is made up of the face you click in followed by which rotation that face undergoes. <br><br />
If you wanted to make the F face of the T cell become the U face of the T cell, that would be Tx because it's rotating the T cell clockwise along the x axis. <br><br />
One of the downsides of this notation is that edge and corner twist moves become longer. For example: T[UF] becomes Tz2x. <br><br />
<br />
===Experimental Notations:===<br />
'''Blob Notation:'''<br />
<br><br />
'''<br />
<br />
===Uncommon/old Notations:===<br />
<br />
'''Roice Notation:''' <br><br />
Roice's Notation uses different names for the cells. <br><br />
[[File:RoiceNotation.gif|400px]]<br />
Each cell's stickers are numbered from 1-27 on the 3^3, and after that you state whether you performed a left or right click. <br></div>Blobinatihttp://wiki.superliminal.com/index.php?title=File:RoiceNotation.gif&diff=3378File:RoiceNotation.gif2021-08-27T03:55:32Z<p>Blobinati: </p>
<hr />
<div></div>Blobinatihttp://wiki.superliminal.com/index.php?title=Notation&diff=3377Notation2021-08-27T03:53:31Z<p>Blobinati: Created page with "==n^4:== ===Commonly Used Notations:=== '''Zhao Notation:''' <br> The notation is similar to that of the 3^3. There are 8 cells, six of them using the same letters as that in..."</p>
<hr />
<div>==n^4:==<br />
===Commonly Used Notations:===<br />
<br />
'''Zhao Notation:''' <br><br />
The notation is similar to that of the 3^3. There are 8 cells, six of them using the same letters as that in the 3^3: U (up), D (down), F (front), B (back), R (right), L (left). The near cell which is not visible, is named K, for kata. The far cell, which appears as the innermost cell, is named T, for top. (''Thanks to Neodam22 for pointing out the problem!'') Its name was changed from A to T since ana and kata are easier to confuse with each other than kata and "top".<br><br />
Each cell in turn uses [http://worldcubeassociation.org/regulations/#notation WCA Official Notation] (standard notation).<br><br />
'''The first letter determines the cell to click on. The second letter determines the sticker on the cell (is usually a 2C piece) to click on''' For example: <br><br />
RK means to click the sticker on the right cell that joins to the near cell.<br><br />
TF means to click the sticker on the far cell that joins to the front cell.<br><br />
FT means to click the sticker on the front cell that joins to the far cell.<br><br />
To state a set of all possible turns (clicks) of a cell, X- is used. For example: R- includes RU, RF, RD, RB, RT, and RK.<br><br />
To state a set of all possible turns (clicks) of cells that are joined to the original sticker to be clicked, -X is used. For example, -R includes UR, FR, DR and BR, TR and KR. <br><br />
Slice and wide turns can be notated with the 2c piece that you click on, plus the number you hold down to perform that move. For example, 2RK is like an M', and 12RK is like Rw'. <br><br />
<br />
'''I/O variant of Zhao Notation''' <br> <br />
Some people in the community prefer to use I (Inner) instead of T, and O (Outer) instead of K. <br> <br />
This makes it more obvious which face is which, whereas "Top" can be confused with Up <br><br />
<br />
'''Rotation Notation:'''<br><br />
Rotation Notation uses the same cell names from Zhao's Notation, but uses 3^3 x, y, and z rotations to be more intuitive. <br><br />
Each turn is made up of the face you click in followed by which rotation that face undergoes. <br><br />
If you wanted to make the F face of the T cell become the U face of the T cell, that would be Tx because it's rotating the T cell clockwise along the x axis. <br><br />
One of the downsides of this notation is that edge and corner twist moves become longer. For example: T[UF] becomes Tz2x. <br><br />
<br />
===Experimental Notations:===<br />
'''Blob Notation:'''<br />
<br><br />
'''<br />
<br />
===Uncommon/old Notations:===<br />
<br />
'''Roice Notation:''' <br><br />
Roice's Notation uses different names for the cells. <br><br />
Each cell's stickers are numbered from 1-27 on the 3^3, and after that you state whether you performed a left or right click. <br></div>Blobinatihttp://wiki.superliminal.com/index.php?title=3%5E4&diff=33683^42021-08-26T04:03:40Z<p>Blobinati: /* M slice */</p>
<hr />
<div>==Roice's Method==<br />
Roice's Method is a piece-by-piece solution that uses commutators that successively build on each other to solve one type of piece at a time.<br />
A link to the method can be found here.<br />
[http://www.superliminal.com/cube/solution/solution.htm Ultimate Solution to a 3x3x3x3.] <br><br />
<br />
Additionally, Charles Doan has developed a system to implement this method. The tutorials can be found [https://m.youtube.com/playlist?list=PLt_EqFtx5iHwBkNDgqpdX8oVoRuUJejzR here.]<br />
<br />
<br>Below is notation used by Ray Zhao.<br />
<br />
==Notation==<br />
'''Ray Zhao's Notation:''' <br><br />
The notation is similar to that of the 3^3. There are 8 cells, six of them using the same letters as that in the 3^3: U (up), D (down), F (front), B (back), R (right), L (left). The near cell which is not visible, is named K, for kata. The far cell, which appears as the innermost cell, is named T, for top. (''Thanks to Neodam22 for pointing out the problem!'') Its name was changed from A to T since ana and kata are easier to confuse with each other than kata and "top".<br><br />
Each cell in turn uses [http://worldcubeassociation.org/regulations/#notation WCA Official Notation] (standard notation).<br><br />
'''The first letter determines the cell to click on. The second letter determines the sticker on the cell (is usually a 2C piece) to click on''' For example: <br><br />
RK means to click the sticker on the right cell that joins to the near cell.<br><br />
TF means to click the sticker on the far cell that joins to the front cell.<br><br />
FT means to click the sticker on the front cell that joins to the far cell.<br><br />
To state a set of all possible turns (clicks) of a cell, X- is used. For example: R- includes RU, RF, RD, RB, RT, and RK.<br><br />
To state a set of all possible turns (clicks) of cells that are joined to the original sticker to be clicked, -X is used. For example, -R includes UR, FR, DR and BR, TR and KR. <br><br />
Slice and wide turns can be notated with the 2c piece that you click on, plus the number you hold down to perform that move. For example, 2RK is like an M', and 12RK is like Rw'. <br><br />
'''Rotation Notation:'''<br><br />
This is the 2nd most widely used notation. It uses the same cell names from Zhao's Notation, but uses 3^3 x, y, and z rotations to be more intuitive. <br><br />
If you wanted to make the F face of the T cell become the U face of the T cell, that would be Tx because it's rotating the T cell clockwise along the x axis. <br><br />
One of the downsides of this notation is that edge and corner twist moves become longer. For example: T[UF] becomes Tz2x. <br><br />
===RKT===<br />
RKT is a technique that is used to execute moves that damage fewer pieces. By using RKT, the solver picks a cell that the solver wants to treat i.e. as a 3^3 (If it was a 4^4 you were solving, RKT would treat a cell as a 4^3). The main idea is to only use RK and T- moves.<br> <br />
For example,<br><br />
<ol><br />
<li>On a 3^3, you can do the sune algorithm: R U R' U R U2 R'. This is an OLL algorithm that can be used to orient corners, but is also able to permute edges (while breaking corners).<br />
</li><br />
<li>On a 3^4, if you replace the algorithm above like so: R=RU, U=TU, you can see that the algorithm seems to have moved 3x1x1x1 blocks. That means that 2c, 3c and 4c are all moved. What if you only want to affect the 3c and 4c of the top 3x3x1x1 block of the T cell? (aka the TU ridge)<br />
</li><br />
<li>Well, back on the 3^3, you can execute sune by doing only R turns and cube rotations. This becomes R z R z' R' z R z' R z R2 z' R'. Notice that the z turn brings the U face into the position of the R face, and the z' turn brings back the original R face.<br />
</li><br />
<li>Now to convert the 3^3 algorithm from the previous step into an RKT algorithm, just substitute R=RK and z=TF. Notice how the T cell seems to be affected in the exact same way the 3^3 was affected in the last step; treating the T cell as a 3^3, it seems to undergo z and R turns. <br />
</li><br />
</ol><br><br />
Note that even though this method is called RKT, it is not limited to those types of turns. Thus, you can use LK and T- moves instead, or rotate your view and use RU and D- instead of RK and T-!<br />
<br />
==Sheerin-Zhao Method (Hybrid) V1==<br />
This method is an attempt to make a 4D analogue of the Fridrich/CFOP method. Using this method results in around 650 to 900 moves, even if no shortcut turns are used. This method needs significant improvement because of the move count required for the last layer. <br />
<br />
===Prerequisites===<br />
<ul><br />
<li>Knowledge of how the cube rotates.</li><br />
<li>The Fridrich Method (F2L/OLL/PLL). 2-look OLL/PLL is enough.</li><br />
<li>Some commutators, especially the monoflip. (R' D' R D R' D R and its inverse)</li><br />
<li>The notation described above</li><br />
</ul><br />
===Summary of the Method===<br />
<ol><br />
<li>Cross: Make a cross by solving 8 2C pieces on the far cell.</li><br />
<li>F2L: Fill in F2L slots by joining F2L pairs (2C/3C) together and inserting them into their respective slots.</li><br />
<li>S2L: Fill in S2L slots. This is done by moving a 3C piece and its respective 4C piece onto the farthest cell. Then, OLL algorithms are used to orient the pieces so that they can be joined using RKT moves. They are then inserted using modified RKT moves.</li><br />
<li>OLL: Orient the LL 2C pieces, 3C pieces, ''then'' the 4C pieces using OLL-C (corner OLL) algorithms, such as the sune/antisune. Try to get as many corners oriented as possible as well. Setup moves are highly recommended here.</li><br />
<li>Pre-PLL: Permute the 2C of the LL using U-perms. </li><br />
<li>PLL: Solve the LL like a 3^3 by using RKT moves. (The cube is rotated at this stage)</li><br />
<li>Parity: If the "top face" of the LL is 180 degrees off from the rest of the puzzle, use the RKT variant of the 180-degree-CW supercube center algorithm (R U R' U five times, OR L R U2 R' L' U twice).</li><br />
</ol><br />
<br />
===Method===<br />
====Cross====<br />
<ol><br />
<li>Pick the colour that you will be using for the near cell (the cell not inside the viewpoint). In this example, cyan is chosen.</li><br />
<li>Rotate the puzzle so that the cell with that specified colour is now the near cell.</li><br />
<li>Intuitively place all -K (2C face) pieces oriented and permuted correctly.<br><br />
This image shows the solved cross.<br />
<br>[[File:C2.png|400px]]<br />
</li><br />
</ol><br />
<br />
====F2L====<br />
<ol><br />
<li>Find any 2C piece that does not include a sticker with the colour of the far cell (i.e. grey).</li><br />
<li>Find the 3C piece with the stickers that have the same colours of the 2C piece and of the near cell. For example, if the 2C piece's colours were red and yellow and the near cell piece was cyan, the 3C piece would be red, yellow, and cyan.</li><br />
<li>Intuitively align the two pieces so that they lie on the same slice on the far cell.</li><br />
<li>Join the pair together and insert the pair into the slot using -U moves.</li><br />
<li>Repeat 11 more times. <br>Note: It is possible to insert the slot flipped. There are many shortcuts in forming pairs too. The image below shows the flipped pair (white-blue).<br />
<br>[[File:C3a.png|400px]]<br />
</li><br />
<li>Here is what it should look like when you are done:<br />
<br>[[File:C3b.png|400px]]</li><br />
</ol><br />
<br />
====S2L====<br />
<ol><br />
<li>Find any 3C piece that does not include a sticker with the colour of the far cell (i.e. grey).</li><br />
<li>Find its respective 4C piece (see F2L for details).<br><br />
note: try finding pairs that are already on the far cell first.</li><br />
<li>If either piece is already inserted and there are no more pairs on the far cell, go down to step 6 and use the algorithm to take the piece out of the slot.</li><br />
<li>Orient the pieces so that the same colours are on the far cell. Sune and antisune is used. Setup moves and RKT are a must.</li><br />
<li>Join the pair together using RKT moves. Twist the far cell until the pair is aligned as shown below (i.e. the green-orange-white pair on the D cell):<br><br />
[[File:C4a.png|400px]]<br><br />
It is possible for the pair to be oriented in two other ways. Make sure that the side colours of the S2L pair match the colours of the faces. Notice how the green and orange stickers match up with the side.<br />
<li>Now, the piece can be inserted using RKT. In this case, it is in the form of RU and D- instead of RK and T-, since you are treating the D cell as a 3^3. In the example shown above, since it is to the left of the slot from that viewpoint, it can be inserted using: (LU DT LU' DT') (LU' DT LU DT'). The next image shows the pair in place.<br><br />
[[File:C4b.png|400px]]</li><br />
<li>Repeat 7 more times.</li><br />
<li>Here is what it should look like when you are done (By now you should have used at most 450 moves):<br><br />
[[File:C4c.png|400px]]</li><br />
</ol><br />
<br />
====OLL====<br />
<ol><br />
<li>Use -U variants of OLL algorithms to orient the 2C pieces. (e.g. for line, FU RU TU RU' TU' FU')<br><br />
Attempt to orient as many 3C pieces in this step as possible.</li><br />
<li>For any unoriented 3C pieces, orient them using -U variants of corner OLL algorithms such as the sune.<br><br />
Note: if there is only one 3c piece left unoriented (see image below), place it so that it's facing you (see f2l flipped pair pic for reference). <br><br />
Use this algorithm if the piece needs to rotate CW: [RK2 RU' TR2 TU' LT2 LU' TR2 TU']*2. For rotating the other way, just reverse the algorithm.<br><br />
[[File:C5a.png|400px]]</li><br />
<br><br />
<li>Before starting to orient the 4C pieces, rotate the cube so that the up cell is now the far cell (T->U). The next image shows the transformation. (Notice the unoriented 3C piece. That is an error; orient all 3C pieces first!)<br><br />
[[File:C5b.png|400px]]</li><br />
<li>Do U- moves so that the unoriented 4C pieces have their U cell sticker (i.e. grey sticker) NOT on the T cell.</li> <br />
<li>Use RKT variants of corner OLL algorithms to orient the 4C piece. If by the end of the algorithm the right cell isn't aligned with the rest of the puzzle, do TF, turn RK until the right slice realigns, then do TF'. Repeat this step and the previous one until all 4C pieces are oriented.</li><br />
<li>If there is only one 4C piece left unoriented (see image below), place it so that it's facing you (see f2l flipped pair pic for reference). <br><br />
[[File:C5d.png|400px]]<br><br />
Then, do BR', use the RKT variant of the monoflip, and do BR. The monoflip to rotate the U-layer sticker of the FULT piece from the L cell to the U cell is as shown: [R U R' U']*2 L' [U R U' R']*2 L. Do the inverse for the algorithm that rotates the U-layer sticker of the FULT piece from the F cell to the U cell.<br />
</li><br />
<li>When all LL layer pieces have been oriented, the T cell should be one uniform colour. Rotate the puzzle back (U->T). The image below shows the unrotated puzzle.<br />
[[File:C5e.png|400px]]<br />
</li><br />
</ol><br />
<br />
====PLL====<br />
<ol><br />
<li>Do T- moves to match as many 2C pieces as possible (At least 2). Then use the -U variant of the U perms to match the rest. (See the first step of OLL for an example of a -U variant.)<br><br />
[[File:C6a.png|400px]]</li><br />
</li><br />
<li>From here, you use RKT moves to solve the rest of the puzzle like a 3^3. Parity: If the "top face" of the LL is 180 degrees off from the rest of the puzzle, use the RKT variant of the 180-degree-CW supercube center algorithm (R U R' U five times, OR L R U2 R' L' U twice).</li><br />
</ol><br/><br />
Please note that this step is very inefficient and can take up to 200 moves on its own.<br />
==Charles Doanâ€™s Method==<br />
This method consists of blockbuilding, as well as techniques from Roice Nelsonâ€™s method to solve the last few pieces. The method was intended for a low move count, as well as simply to serve as a unique method to solve the 4 dimensional Rubikâ€™s Cube. Using this method as a beginner is strongly advised against. There will be complex concepts that will be very difficult to grasp, therefore it is advised that this method only be utilized by individuals who have relatively proficient experience for the 3^4 cube. This method will be making use of the notation established by Raymond Zhao.<br />
<br />
===Prerequisites===<br />
<ol><br />
<li> To know how to solve the 4D Rubikâ€™s Cube using Roice Nelsonâ€™s method.<br />
<li> To be proficient at blockbuilding on a normal Rubikâ€™s Cube.<br />
<li> To have adequate experience for the 4D Rubikâ€™s Cube.<br />
</ol><br />
===Steps===<br />
<ol><br />
<li> Solve a 2*2*2*2 cube.<br />
<li> Expand the block to a 2*2*3*2.<br />
<li> Create a full or semi-F2L on the inner face.<br />
<li> Solve the First 2 Layers with or without missing 4-coloreds.<br />
<li> Solve the remaining pieces using Roice Nelsonâ€™s piece-by-piece method or Raymond Zhaoâ€™s OLL/PLL approach.<br />
</ol><br />
<br />
==Octachoroux Method==<br />
This method is the 4 dimensional equivalent of the Roux method. It aims for a more intuitive blockbuilding approach, as well as less algorithms needed to be memorized. The name Octachoroux comes from the word octachoron (which is another word for tesseract) and Roux.<br />
<br />
===Prerequisites===<br />
<ul><br />
<li> Knowledge of how the puzzle turns, and Zhao Notation </li><br />
<li> Knowledge of blockbuilding and the Roux method on the 3^3 </li><br />
<li> Knowledge of names of 4d pieces and the concept of RKT </li><br />
</ul><br />
<br />
===Summary of the Method:===<br />
<ul><br />
<li> First Block: Solve a 1x2x3x3 block using blockbuilding techniques </li><br />
<li> Second Block: Solve a 1x2x3x3 on the other side of the puzzle to complete your First 2 Blocks </li><br />
<li> CMLC: Orient and permute the corners of the U cell </li><br />
<li> L/R: Solve the Left and Right cells </li><br />
<li> M Slice: Permute the M slice </li><br />
</ul><br />
<br />
===First Block===<br />
Pick the colour of which first block you will be starting with. If you normally start with White or Yellow on D and any colour on the side, that would make you x2yw colour neutral. <br><br />
Build a 1x2x3x3 block. You could solve the 2c pieces first, and then use the K cell to easily pair up pieces without disturbing your progress on the T cell. Then you can just bring those pairs onto the T cell and insert them using -K moves as normal 3^3 twists. <br><br />
Once this step is completed, hold the first block on the left, just as in normal Roux. <br><br />
[[File:Firstblock_2.png|400px]] [[File:Firstblock_1.png|400px]]<br />
<br />
===Second Block===<br />
Make the same 1x2x3x3 block, just on the other side. Start with the DR 2c piece. After that you can solve the other 4 2c pieces by bringing them to TU and doing RF TF' RF' to insert them. You can use many of the same tricks from the 3^3, such as hiding an edge in TDF and then rotating the U cell to bring the corner the edge pairs up with onto the T cell, then connecting them with M moves. RKT is necessary to insert pairs without messing up the first block. <br><br />
[[File:Secondblock.png|400px]]<br />
<br />
===CMLC (CO)===<br />
Bring the U cell to T, then use RKT to set up a layer so that it looks like a normal OCLL case, then bring the T cell to U. Hold that case so that it is in the D layer of the U cell, as shown in the image below, and use RKT variants of OCLL algorithms to orient those pieces. <br><br />
[[File:CMLC_CO1.png|400px]] <br><br />
Repeat this until all the corners are oriented. If you just have 1 corner left to twist, a good intuitive way to do this is to untwist 2 other corners, then use RKT to set that up in to a Sune case. You can also use the Monoflip algorithm described in the Sheerin-Zhao method above. <br><br />
[[File:CMLC_CO2.png||400px]]<br />
<br />
===CMLC (CP)===<br />
Now bring the U cell to T and use RKT to permute it like a regular 2x2x2 Rubik's cube. If you get a parity where a layer ends up being off by 180 degrees, use the RKT parity algorithm: <br><br />
TU UR T[LFU]' UK' TF RF UR RF' U[TR] <br><br />
It will look like this when it is done. Rotate the T cell back to the U cell <br><br />
[[File:CMLC_CP2.png|400px]]<br />
<br />
===L/R===<br />
Instead of orienting the edges like in 3^3 Roux, just go directly to solving the Left and Right cells of the cube. The reason why will become apparent later. <br><br />
First solve the 2c pieces with the L/R and U colour. <br><br />
Now you setup edges that need to go to L/R into the TDF spot with the L/R colour on the T cell and the U colour on the D cell. Then move the spot where that L/R edge needs to go above that edge and insert that piece using the RKT algorithm of M D2 M' D2 (2RK' TF' RK2 TF 2RK TF' RK2 TF) <br><br />
[[File:LR2.png|400px]] <br><br />
There are 8 edges total that need to be inserted for L/R do be complete.<br />
<br />
===M slice===<br />
[[File:M1.png|400px]] <br><br />
Now all you have to do is permute the M slice. This step is pretty similar to PLL from Sheerin-Zhao method, but with some key differences. <br><br />
<ul><br />
<li> Pieces have the same number of colours as they do on the 3^3. Corners pieces have 3, edges have 2, etc. </li><br />
<li> Pieces can look "mirrored" </li><br />
<li> There is no RKT parity </li><br />
</ul><br />
Now you can either use UR moves as U, U', U2 moves, and M slice rotations to do RKT (called URM), or rotate to bring one of the L/R sides to the T cell and use normal RKT, except you have to hold down 2 on your keyboard in order to do T moves. <br><br />
There are some interesting "parities" you might encounter that are impossible on both the 3^3, and the 3^3 last layer of CFOP 3^4. Such as: <br><br />
<ul><br />
<li> Corner pieces that look "mirrored" </li><br />
<li> Impossible Last Layer/CMLL(/whatever method you use) cases </li><br />
</ul><br />
If you solve the M slice using CFOP, then once you get to PLL, you can rotate the puzzle so that the U cell goes to T, and then orient the edges onto the T cell and then permute that like step 4c of the Roux method. <br><br />
If you solve the M slice using Roux, then look forward to impossible CO and CP cases from 2-look CMLL. <br><br />
An algorithm that is super useful here is a pure 2-flip of 3c pieces. I use M' U M' U M' U M' U2 M' U M' U M' U M' using RKT.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=3%5E4&diff=33673^42021-08-26T04:02:51Z<p>Blobinati: </p>
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<div>==Roice's Method==<br />
Roice's Method is a piece-by-piece solution that uses commutators that successively build on each other to solve one type of piece at a time.<br />
A link to the method can be found here.<br />
[http://www.superliminal.com/cube/solution/solution.htm Ultimate Solution to a 3x3x3x3.] <br><br />
<br />
Additionally, Charles Doan has developed a system to implement this method. The tutorials can be found [https://m.youtube.com/playlist?list=PLt_EqFtx5iHwBkNDgqpdX8oVoRuUJejzR here.]<br />
<br />
<br>Below is notation used by Ray Zhao.<br />
<br />
==Notation==<br />
'''Ray Zhao's Notation:''' <br><br />
The notation is similar to that of the 3^3. There are 8 cells, six of them using the same letters as that in the 3^3: U (up), D (down), F (front), B (back), R (right), L (left). The near cell which is not visible, is named K, for kata. The far cell, which appears as the innermost cell, is named T, for top. (''Thanks to Neodam22 for pointing out the problem!'') Its name was changed from A to T since ana and kata are easier to confuse with each other than kata and "top".<br><br />
Each cell in turn uses [http://worldcubeassociation.org/regulations/#notation WCA Official Notation] (standard notation).<br><br />
'''The first letter determines the cell to click on. The second letter determines the sticker on the cell (is usually a 2C piece) to click on''' For example: <br><br />
RK means to click the sticker on the right cell that joins to the near cell.<br><br />
TF means to click the sticker on the far cell that joins to the front cell.<br><br />
FT means to click the sticker on the front cell that joins to the far cell.<br><br />
To state a set of all possible turns (clicks) of a cell, X- is used. For example: R- includes RU, RF, RD, RB, RT, and RK.<br><br />
To state a set of all possible turns (clicks) of cells that are joined to the original sticker to be clicked, -X is used. For example, -R includes UR, FR, DR and BR, TR and KR. <br><br />
Slice and wide turns can be notated with the 2c piece that you click on, plus the number you hold down to perform that move. For example, 2RK is like an M', and 12RK is like Rw'. <br><br />
'''Rotation Notation:'''<br><br />
This is the 2nd most widely used notation. It uses the same cell names from Zhao's Notation, but uses 3^3 x, y, and z rotations to be more intuitive. <br><br />
If you wanted to make the F face of the T cell become the U face of the T cell, that would be Tx because it's rotating the T cell clockwise along the x axis. <br><br />
One of the downsides of this notation is that edge and corner twist moves become longer. For example: T[UF] becomes Tz2x. <br><br />
===RKT===<br />
RKT is a technique that is used to execute moves that damage fewer pieces. By using RKT, the solver picks a cell that the solver wants to treat i.e. as a 3^3 (If it was a 4^4 you were solving, RKT would treat a cell as a 4^3). The main idea is to only use RK and T- moves.<br> <br />
For example,<br><br />
<ol><br />
<li>On a 3^3, you can do the sune algorithm: R U R' U R U2 R'. This is an OLL algorithm that can be used to orient corners, but is also able to permute edges (while breaking corners).<br />
</li><br />
<li>On a 3^4, if you replace the algorithm above like so: R=RU, U=TU, you can see that the algorithm seems to have moved 3x1x1x1 blocks. That means that 2c, 3c and 4c are all moved. What if you only want to affect the 3c and 4c of the top 3x3x1x1 block of the T cell? (aka the TU ridge)<br />
</li><br />
<li>Well, back on the 3^3, you can execute sune by doing only R turns and cube rotations. This becomes R z R z' R' z R z' R z R2 z' R'. Notice that the z turn brings the U face into the position of the R face, and the z' turn brings back the original R face.<br />
</li><br />
<li>Now to convert the 3^3 algorithm from the previous step into an RKT algorithm, just substitute R=RK and z=TF. Notice how the T cell seems to be affected in the exact same way the 3^3 was affected in the last step; treating the T cell as a 3^3, it seems to undergo z and R turns. <br />
</li><br />
</ol><br><br />
Note that even though this method is called RKT, it is not limited to those types of turns. Thus, you can use LK and T- moves instead, or rotate your view and use RU and D- instead of RK and T-!<br />
<br />
==Sheerin-Zhao Method (Hybrid) V1==<br />
This method is an attempt to make a 4D analogue of the Fridrich/CFOP method. Using this method results in around 650 to 900 moves, even if no shortcut turns are used. This method needs significant improvement because of the move count required for the last layer. <br />
<br />
===Prerequisites===<br />
<ul><br />
<li>Knowledge of how the cube rotates.</li><br />
<li>The Fridrich Method (F2L/OLL/PLL). 2-look OLL/PLL is enough.</li><br />
<li>Some commutators, especially the monoflip. (R' D' R D R' D R and its inverse)</li><br />
<li>The notation described above</li><br />
</ul><br />
===Summary of the Method===<br />
<ol><br />
<li>Cross: Make a cross by solving 8 2C pieces on the far cell.</li><br />
<li>F2L: Fill in F2L slots by joining F2L pairs (2C/3C) together and inserting them into their respective slots.</li><br />
<li>S2L: Fill in S2L slots. This is done by moving a 3C piece and its respective 4C piece onto the farthest cell. Then, OLL algorithms are used to orient the pieces so that they can be joined using RKT moves. They are then inserted using modified RKT moves.</li><br />
<li>OLL: Orient the LL 2C pieces, 3C pieces, ''then'' the 4C pieces using OLL-C (corner OLL) algorithms, such as the sune/antisune. Try to get as many corners oriented as possible as well. Setup moves are highly recommended here.</li><br />
<li>Pre-PLL: Permute the 2C of the LL using U-perms. </li><br />
<li>PLL: Solve the LL like a 3^3 by using RKT moves. (The cube is rotated at this stage)</li><br />
<li>Parity: If the "top face" of the LL is 180 degrees off from the rest of the puzzle, use the RKT variant of the 180-degree-CW supercube center algorithm (R U R' U five times, OR L R U2 R' L' U twice).</li><br />
</ol><br />
<br />
===Method===<br />
====Cross====<br />
<ol><br />
<li>Pick the colour that you will be using for the near cell (the cell not inside the viewpoint). In this example, cyan is chosen.</li><br />
<li>Rotate the puzzle so that the cell with that specified colour is now the near cell.</li><br />
<li>Intuitively place all -K (2C face) pieces oriented and permuted correctly.<br><br />
This image shows the solved cross.<br />
<br>[[File:C2.png|400px]]<br />
</li><br />
</ol><br />
<br />
====F2L====<br />
<ol><br />
<li>Find any 2C piece that does not include a sticker with the colour of the far cell (i.e. grey).</li><br />
<li>Find the 3C piece with the stickers that have the same colours of the 2C piece and of the near cell. For example, if the 2C piece's colours were red and yellow and the near cell piece was cyan, the 3C piece would be red, yellow, and cyan.</li><br />
<li>Intuitively align the two pieces so that they lie on the same slice on the far cell.</li><br />
<li>Join the pair together and insert the pair into the slot using -U moves.</li><br />
<li>Repeat 11 more times. <br>Note: It is possible to insert the slot flipped. There are many shortcuts in forming pairs too. The image below shows the flipped pair (white-blue).<br />
<br>[[File:C3a.png|400px]]<br />
</li><br />
<li>Here is what it should look like when you are done:<br />
<br>[[File:C3b.png|400px]]</li><br />
</ol><br />
<br />
====S2L====<br />
<ol><br />
<li>Find any 3C piece that does not include a sticker with the colour of the far cell (i.e. grey).</li><br />
<li>Find its respective 4C piece (see F2L for details).<br><br />
note: try finding pairs that are already on the far cell first.</li><br />
<li>If either piece is already inserted and there are no more pairs on the far cell, go down to step 6 and use the algorithm to take the piece out of the slot.</li><br />
<li>Orient the pieces so that the same colours are on the far cell. Sune and antisune is used. Setup moves and RKT are a must.</li><br />
<li>Join the pair together using RKT moves. Twist the far cell until the pair is aligned as shown below (i.e. the green-orange-white pair on the D cell):<br><br />
[[File:C4a.png|400px]]<br><br />
It is possible for the pair to be oriented in two other ways. Make sure that the side colours of the S2L pair match the colours of the faces. Notice how the green and orange stickers match up with the side.<br />
<li>Now, the piece can be inserted using RKT. In this case, it is in the form of RU and D- instead of RK and T-, since you are treating the D cell as a 3^3. In the example shown above, since it is to the left of the slot from that viewpoint, it can be inserted using: (LU DT LU' DT') (LU' DT LU DT'). The next image shows the pair in place.<br><br />
[[File:C4b.png|400px]]</li><br />
<li>Repeat 7 more times.</li><br />
<li>Here is what it should look like when you are done (By now you should have used at most 450 moves):<br><br />
[[File:C4c.png|400px]]</li><br />
</ol><br />
<br />
====OLL====<br />
<ol><br />
<li>Use -U variants of OLL algorithms to orient the 2C pieces. (e.g. for line, FU RU TU RU' TU' FU')<br><br />
Attempt to orient as many 3C pieces in this step as possible.</li><br />
<li>For any unoriented 3C pieces, orient them using -U variants of corner OLL algorithms such as the sune.<br><br />
Note: if there is only one 3c piece left unoriented (see image below), place it so that it's facing you (see f2l flipped pair pic for reference). <br><br />
Use this algorithm if the piece needs to rotate CW: [RK2 RU' TR2 TU' LT2 LU' TR2 TU']*2. For rotating the other way, just reverse the algorithm.<br><br />
[[File:C5a.png|400px]]</li><br />
<br><br />
<li>Before starting to orient the 4C pieces, rotate the cube so that the up cell is now the far cell (T->U). The next image shows the transformation. (Notice the unoriented 3C piece. That is an error; orient all 3C pieces first!)<br><br />
[[File:C5b.png|400px]]</li><br />
<li>Do U- moves so that the unoriented 4C pieces have their U cell sticker (i.e. grey sticker) NOT on the T cell.</li> <br />
<li>Use RKT variants of corner OLL algorithms to orient the 4C piece. If by the end of the algorithm the right cell isn't aligned with the rest of the puzzle, do TF, turn RK until the right slice realigns, then do TF'. Repeat this step and the previous one until all 4C pieces are oriented.</li><br />
<li>If there is only one 4C piece left unoriented (see image below), place it so that it's facing you (see f2l flipped pair pic for reference). <br><br />
[[File:C5d.png|400px]]<br><br />
Then, do BR', use the RKT variant of the monoflip, and do BR. The monoflip to rotate the U-layer sticker of the FULT piece from the L cell to the U cell is as shown: [R U R' U']*2 L' [U R U' R']*2 L. Do the inverse for the algorithm that rotates the U-layer sticker of the FULT piece from the F cell to the U cell.<br />
</li><br />
<li>When all LL layer pieces have been oriented, the T cell should be one uniform colour. Rotate the puzzle back (U->T). The image below shows the unrotated puzzle.<br />
[[File:C5e.png|400px]]<br />
</li><br />
</ol><br />
<br />
====PLL====<br />
<ol><br />
<li>Do T- moves to match as many 2C pieces as possible (At least 2). Then use the -U variant of the U perms to match the rest. (See the first step of OLL for an example of a -U variant.)<br><br />
[[File:C6a.png|400px]]</li><br />
</li><br />
<li>From here, you use RKT moves to solve the rest of the puzzle like a 3^3. Parity: If the "top face" of the LL is 180 degrees off from the rest of the puzzle, use the RKT variant of the 180-degree-CW supercube center algorithm (R U R' U five times, OR L R U2 R' L' U twice).</li><br />
</ol><br/><br />
Please note that this step is very inefficient and can take up to 200 moves on its own.<br />
==Charles Doanâ€™s Method==<br />
This method consists of blockbuilding, as well as techniques from Roice Nelsonâ€™s method to solve the last few pieces. The method was intended for a low move count, as well as simply to serve as a unique method to solve the 4 dimensional Rubikâ€™s Cube. Using this method as a beginner is strongly advised against. There will be complex concepts that will be very difficult to grasp, therefore it is advised that this method only be utilized by individuals who have relatively proficient experience for the 3^4 cube. This method will be making use of the notation established by Raymond Zhao.<br />
<br />
===Prerequisites===<br />
<ol><br />
<li> To know how to solve the 4D Rubikâ€™s Cube using Roice Nelsonâ€™s method.<br />
<li> To be proficient at blockbuilding on a normal Rubikâ€™s Cube.<br />
<li> To have adequate experience for the 4D Rubikâ€™s Cube.<br />
</ol><br />
===Steps===<br />
<ol><br />
<li> Solve a 2*2*2*2 cube.<br />
<li> Expand the block to a 2*2*3*2.<br />
<li> Create a full or semi-F2L on the inner face.<br />
<li> Solve the First 2 Layers with or without missing 4-coloreds.<br />
<li> Solve the remaining pieces using Roice Nelsonâ€™s piece-by-piece method or Raymond Zhaoâ€™s OLL/PLL approach.<br />
</ol><br />
<br />
==Octachoroux Method==<br />
This method is the 4 dimensional equivalent of the Roux method. It aims for a more intuitive blockbuilding approach, as well as less algorithms needed to be memorized. The name Octachoroux comes from the word octachoron (which is another word for tesseract) and Roux.<br />
<br />
===Prerequisites===<br />
<ul><br />
<li> Knowledge of how the puzzle turns, and Zhao Notation </li><br />
<li> Knowledge of blockbuilding and the Roux method on the 3^3 </li><br />
<li> Knowledge of names of 4d pieces and the concept of RKT </li><br />
</ul><br />
<br />
===Summary of the Method:===<br />
<ul><br />
<li> First Block: Solve a 1x2x3x3 block using blockbuilding techniques </li><br />
<li> Second Block: Solve a 1x2x3x3 on the other side of the puzzle to complete your First 2 Blocks </li><br />
<li> CMLC: Orient and permute the corners of the U cell </li><br />
<li> L/R: Solve the Left and Right cells </li><br />
<li> M Slice: Permute the M slice </li><br />
</ul><br />
<br />
===First Block===<br />
Pick the colour of which first block you will be starting with. If you normally start with White or Yellow on D and any colour on the side, that would make you x2yw colour neutral. <br><br />
Build a 1x2x3x3 block. You could solve the 2c pieces first, and then use the K cell to easily pair up pieces without disturbing your progress on the T cell. Then you can just bring those pairs onto the T cell and insert them using -K moves as normal 3^3 twists. <br><br />
Once this step is completed, hold the first block on the left, just as in normal Roux. <br><br />
[[File:Firstblock_2.png|400px]] [[File:Firstblock_1.png|400px]]<br />
<br />
===Second Block===<br />
Make the same 1x2x3x3 block, just on the other side. Start with the DR 2c piece. After that you can solve the other 4 2c pieces by bringing them to TU and doing RF TF' RF' to insert them. You can use many of the same tricks from the 3^3, such as hiding an edge in TDF and then rotating the U cell to bring the corner the edge pairs up with onto the T cell, then connecting them with M moves. RKT is necessary to insert pairs without messing up the first block. <br><br />
[[File:Secondblock.png|400px]]<br />
<br />
===CMLC (CO)===<br />
Bring the U cell to T, then use RKT to set up a layer so that it looks like a normal OCLL case, then bring the T cell to U. Hold that case so that it is in the D layer of the U cell, as shown in the image below, and use RKT variants of OCLL algorithms to orient those pieces. <br><br />
[[File:CMLC_CO1.png|400px]] <br><br />
Repeat this until all the corners are oriented. If you just have 1 corner left to twist, a good intuitive way to do this is to untwist 2 other corners, then use RKT to set that up in to a Sune case. You can also use the Monoflip algorithm described in the Sheerin-Zhao method above. <br><br />
[[File:CMLC_CO2.png||400px]]<br />
<br />
===CMLC (CP)===<br />
Now bring the U cell to T and use RKT to permute it like a regular 2x2x2 Rubik's cube. If you get a parity where a layer ends up being off by 180 degrees, use the RKT parity algorithm: <br><br />
TU UR T[LFU]' UK' TF RF UR RF' U[TR] <br><br />
It will look like this when it is done. Rotate the T cell back to the U cell <br><br />
[[File:CMLC_CP2.png|400px]]<br />
<br />
===L/R===<br />
Instead of orienting the edges like in 3^3 Roux, just go directly to solving the Left and Right cells of the cube. The reason why will become apparent later. <br><br />
First solve the 2c pieces with the L/R and U colour. <br><br />
Now you setup edges that need to go to L/R into the TDF spot with the L/R colour on the T cell and the U colour on the D cell. Then move the spot where that L/R edge needs to go above that edge and insert that piece using the RKT algorithm of M D2 M' D2 (2RK' TF' RK2 TF 2RK TF' RK2 TF) <br><br />
[[File:LR2.png|400px]] <br><br />
There are 8 edges total that need to be inserted for L/R do be complete.<br />
<br />
===M slice===<br />
[[File:M1.png|400px]]<br />
Now all you have to do is permute the M slice. This step is pretty similar to PLL from Sheerin-Zhao method, but with some key differences. <br><br />
<ul><br />
<li> Pieces have the same number of colours as they do on the 3^3. Corners pieces have 3, edges have 2, etc. </li><br />
<li> Pieces can look "mirrored" </li><br />
<li> There is no RKT parity </li><br />
</ul><br />
Now you can either use UR moves as U, U', U2 moves, and M slice rotations to do RKT (called URM), or rotate to bring one of the L/R sides to the T cell and use normal RKT, except you have to hold down 2 on your keyboard in order to do T moves. <br><br />
There are some interesting "parities" you might encounter that are impossible on both the 3^3, and the 3^3 last layer of CFOP 3^4. Such as: <br><br />
<ul><br />
<li> Corner pieces that look "mirrored" </li><br />
<li> Impossible Last Layer/CMLL(/whatever method you use) cases </li><br />
</ul><br />
If you solve the M slice using CFOP, then once you get to PLL, you can rotate the puzzle so that the U cell goes to T, and then orient the edges onto the T cell and then permute that like step 4c of the Roux method. <br><br />
If you solve the M slice using Roux, then look forward to impossible CO and CP cases from 2-look CMLL. <br><br />
An algorithm that is super useful here is a pure 2-flip of 3c pieces. I use M' U M' U M' U M' U2 M' U M' U M' U M' using RKT.</div>Blobinatihttp://wiki.superliminal.com/index.php?title=File:M1.png&diff=3366File:M1.png2021-08-26T04:02:14Z<p>Blobinati: </p>
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