3^4

Roice Method

This method is the 4D version of the "ultimate solution for the rubik's cube's.
check it out here: [1]

Notation

View-based

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" and "far" cells are named A (ana) and K (kata), respectively.
Each cell in turn uses WCA Official Notation (standard notation).
The cell to be rotated is first stated, followed by the rotation. For example:
RR means to click the right face of the right cell.
AF means to click the front face of the far cell.
To state general moves (move subsets), use -. For example: R- means the set of all possible turns of the right cell.
<RR,A-> moves mean to only use RR and A moves. This method is used by Matthew Sheerin.

Face-Based

The letters are the same as that for view-based notation, but the second letter is determined by the face the piece to turn is connected to. For example:
RR is invalid. RA means to click the face connecting the right cell to the far one.
AF means to click the face connecting the far cell to the front cell.
Order does not matter in face-based notation.

Sheerin-Zhao Method (Hybrid)

This method is an attempt to make a 4D analogue of the Friedrich, or 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.

Prerequisites

• Knowledge of how the cube rotates.
• The Friedrich Method (F2L/OLL/PLL). 2-look OLL/PLL is enough.

Summary of the Method

1. Cross: Make a cross by solving 8 2C pieces on the far cell.
2. F2L: Fill in F2L slots by joining F2L pairs (2C/3C) together and inserting them into their respective slots.
3. S2L: Fill in S2L slots. This is done by moving a 3C piece and its respective 4C piece onto the farthest cell (i.e. the last layer). Then, OLL algorithms are used to orient the pieces so that they can be joined using <RR, A-> moves. They are then inserted by using more <RR, A-> moves.
4. OLL: Orient the LL 2C pieces, then the 3C 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.
5. Pre-PLL: Permute the 2C of the LL using U-perms.
6. PLL: Solve the LL like a 3^3 by using <RR,A-> moves.
7. Parity: If the "top face" of the LL is 180 degrees off from the rest of the puzzle, use the <RR,A-> variant of the supercube centers algorithm (R U R' U five times)