Professors Cube/Layer Method
From charlesreid1
Solution Algorithm Steps
Step 1: Center Crosses
Form the crosses on each respective cube face.
Work on opposite colors, in pairs. Start with yellow cross, then do white cross on opposite face. Do red-then-orange, and blue-then-green.
Like the 3x3 step of forming a cross, this step utilizes a few algorithms that are simple enough to work out through trial and error - nothing very tricky.
Step 2: Center Faces
The goal of the second step is to make all nine cubies on the center faces the correct color.
(Note that because of the odd parity of the cube, and in contrast to the 4x4, the center pieces are fixed in place, so no extra checking is required to ensure the faces are correctly oriented.)
Algorithm for adjacent faces:
Use the algorithm below to exchange the cubies on the corners of the center of the face (the non-cross face cubies) until each face of the cube has a solid 3x3 face of a single color.
The algorithm to swap corner cubies on faces:
l F l' F l F F l' F F
This algorithm will swap the corner cubie on the top left of the front face with the corner cubie on the bottom left of the top face.
The following diagram shows an asterisk on the two cubies that will be swapped:
____________________
/___/___/___/___/___/
/___/___/___/___/___/
/___/___/___/___/___/
/___/_*_/___/___/___/
/___/___/___/___/___/
| | | | | |
|___|___|___|___|___|
| | * | | | |
|___|___|___|___|___|
| | | | | |
|___|___|___|___|___|
| | | | | |
|___|___|___|___|___|
| | | | | |
|___|___|___|___|___|
Algorithm for opposite faces:
This algorithm will swap the top right cubie on a given face with its corresponding cubie on the opposite face of the cube. White swaps with yellow, blue swaps with green, red swaps with orange. Without this algorithm, you'd have to perform the above algorithm for adjacent faces at least twice to move the corner cubie from face to face.
The algorithm is:
(Rr)2 B (Rr)2 B (Rr)2 B B (Rr)2 B B
This is the cubie that will be swapped:
____________________
/___/___/___/___/___/
/___/___/___/___/___/
/___/___/___/___/___/
/___/___/___/___/___/
/___/___/___/___/___/
| | | | | |
|___|___|___|___|___|
| | | | * | |
|___|___|___|___|___|
| | | | | |
|___|___|___|___|___|
| | | | | |
|___|___|___|___|___|
| | | | | |
|___|___|___|___|___|
Step 3: Align Triple-Edges
Use algorithms to line up triple edges so that they are all of a single color combination.
Proceed as follows:
- Line up the three cubies in a triple edge and "store" it on the top of the cube.
- Repeat the above procedure until all 4 triple-edges of the top face are solved (meaning, the three cubies of the triple edge have matching colors and orientations).
- Flip the cube upside down and repeat the above procedure, so that eight total triple edges (four on the top and four on the bottom) are solved.
- With the cube oriented such that the top and bottom faces have all their triple edges solved, rotate the back face once and solve the two triple edges in the front.
- Solve the last remaining two triple edges using the algorithm from the 4x4 Rubiks Revenge that brings together two edge pieces that are on opposite sides/ends of a face (see the Rubiks Revenge#Algorithms section for this edge-swapping algorithm).
This step should conclude with either zero, one, or two triple edges that have their center cubie oriented inside out from the other two cubies.
Step 4: Correct Triple Edge Orientation
If Step 3 concluded with zero triple edges that have their center cubie oriented inside-out, skip this step and proceed to solve the 5x5 cube using 3x3 algorithms.
If Step 3 concluded with one triple edge that has its center cubie oriented inside-out, apply the Triple Edge Flip algorithm:
(TODO: Add algorithm, pictures)
If Step 3 concluded with two triple edges that have their center cubies oriented inside-out, apply the Edge Swap algorithm from the 4x4:
(TODO: Add the edge-swap algorithm here and expand on it to use the correct notation for the 5x5)
(TODO: pictures of before/after, and which face and algorithm)
(TODO: Revisit the other pages' solution methods and name the algorithms; Edge Swapping algorithm, Double Edge Flip algorithm, etc.)
Apply the Holy Cube Algorithm:
(Rr)2 B2 U2 (Ll) U2 (Rr)' U2 (Rr) U2 F2 (Rr) F2 (Ll)' B2 (Rr)2
Step 5: Solve the 3x3
Once all 12 triple-edges are correctly oriented, the cube is in an equivalent 3x3 state, where the center nine face cubies are equivalent to the 3x3 cube's single face cubie, and each triple-edge is equivalent to a single edge piece on the 3x3 cube.
All center pieces are a solid square of nine colors, and all triple edges are aligned, so the cube is now in a state that is exactly equivalent to a 3x3 Rubik's Cube. You should now be able to tear through the remainder of the solve in the classical manner (yellow cross - yellow face - second layer - top cross - cycle corner cubies - orient corner cubies).
For more detail about each step, see the Professors Cube page.
Algorithms Cheat Sheet
Patterns
It is also possible to apply algorithms to the solved Professor's Cube to create various interesting patterns.
Simulator
https://ruwix.com/online-puzzle-simulators/5x5x5-professors-cube-simulator.php
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