# Professors Cube/Layer Method

### From charlesreid1

## Contents

## 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

Use an algorithm 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.

(Note that, unlike the 4x4, the center pieces are fixed, so the faces will be correctly oriented and no extra checking is required.)

### 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.

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