Professors Cube

Mathematical Representation

Like the 3x3 and 4x4 cubes, the 5x5 cube can be represented using a tuple, with one entry in the tuple per face of the cube.

The 3x3 cube has 3^2 = 9 faces per side, for a total of 6 x 9 = 54 faces, so the state of any 3x3 cube can be represented using a 54-uple.

The 4x4 cube has 4^2 = 16 faces per side, for a total of 6 x 16 = 96 faces, so the state of any 4x4 cube can be represented using a 96-uple.

The 5x5 cube has 5^2 = 25 faces per side, for a total of 6 x 25 = 150 faces, so we can write the state of any 5x5 cube using a 150-uple.

For general information on the mathematical representation of the cube:

• Rubiks Cube/Tuple
• Rubiks Cube/Permutations

For information specific to the 5x5 cube:

• Professors Cube/Numbers - counting the various possible states of a 5x5 cube
• Professors Cube/Tuple - representing the various possible states of a 5x5 cube in unique ways
• Professors Cube/Permutations - utilizing permutation algebra to manipulate the 5x5 cube

References

Not much here: https://www.speedsolving.com/wiki/index.php/Category:5x5x5_methods