Difference between revisions of "Physical Puzzle"
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[[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]] | [[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]] | ||
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== 3D Physical Puzzles == | == 3D Physical Puzzles == | ||
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Revision as of 12:31, 5 September 2022
Contents
Definition
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.
2D Physical Puzzles
When designing 3D physical puzzle 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. 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, which will make certain moves inaccessible without the use of a gyro. We can see that in the 2^4 case we can have the cubies cube shaped because by mathematical coincidence a cube has 4 fold symmetry(a 2^4 cubie has 4 colors).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.
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 if you squint a little bit it 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 it's canonical moves(rotate 3C pieces with it's 2Cs, by first making sure all its associated 2Cs are touching it). By the same logic one can construct a 3D physical simplex.
3D Physical Puzzles
The first physical puzzle was the 2^4 designed by Melinda Green in 2017. After this Grant, Luna, Hactar and 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 2x2x3x3. There where attempts at designing shapeshifting physical puzzles with no success.
3D Physical designs list
2^4-Melinda Green | 2017
2x2x2x3-Luna | December 2021
2x2x3x3-Grant and Hactar | May 2022
2x3x3x3-Luna and Hactar
1x2x2x2, 1x2x2x3, 1x2x3x3, 1x3x3x3-Grant
3x3 Simplex and Bandaged Void Simplex-Markk | August 2022
Physical Shapeshifting Puzzles
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.
