## 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.)

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 the Triple Edge Orientation

There are three ways Step 3 can end.

The first and easiest way is if there are no triple edges that are oriented "inside out" (the middle cubie is of the opposite orientation from its two neighbor cubies).

The second way is if one triple edge is oriented inside out, which requires a new algorithm exclusive to the 5x5 cube.

The third way is if two triple edges are oriented inside out.

#### No Inside Out Triple Edges

Congratulations! You're already done with Step 4.

#### One Inside Out Triple Edge

If Step 3 finishes with one triple edge oriented incorrectly (middle cubie is opposite orientation from two neighbor cubies), a new algorithm is needed to flip the middle cubie of one triple edge only.

This is the 5x5 Tredge Flip Algorithm:

```(Rr)2  B2   U2
(Ll)   U2
(Rr)'  U2
(Rr)   U2
F2     (Rr)
F2     (Ll)'
B2     (Rr)2
```

This should be performed with the inside out triple edge at the top front (the cube's "forehead"). All other triple edges should be properly oriented.

#### Two Inside Out Triple Edges

If Step 3 finishes with two triple edges oriented incorrectly (middle cubie is opposite orientation from two neighbor cubies), no new algorithms are needed, you can use the Edge Swapping algorithm (which swaps a cubie between the left and right triple edges) to fix them.

Orient the cube so that the two inside out triple edges are on the left and right edge of the front face. Then execute this algorithm to exchange the bottom cubie of the left triple edge with the top cubie of the right triple edge.

Edge Swapping Algorithm:

```Dd R F' U R' F Dd'
```

Now, make sure that the middle and top cubies of the left triple edge are the same color as the top cubie of the right triple edge. (You may need to flip one of the triple edges.)

From that orientation (middle and top cubies of left triple edge match top cubie of right triple edge), execute the Edge Swapping algorithm again:

```Dd R F' U R' F Dd'
```

This will result in all triple edges being aligned.

(TODO: Revisit the other pages' solution methods and name the algorithms; Edge Swapping algorithm, Double Edge Flip algorithm, etc.)

### 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

5x5 Tredge Flip:

```(Rr)2  B2   U2
(Ll)   U2
(Rr)'  U2
(Rr)   U2
F2     (Rr)
F2     (Ll)'
B2     (Rr)2
```

5x5 Edge Swap:

```Dd R F' U R' F Dd'
```

## Patterns

It is also possible to apply algorithms to the solved Professor's Cube to create various interesting patterns.