Math
Rubik's cube as a group
Treat a Rubik cube as exact facelet permutations. Animate products, inverses, conjugation and a commutator, then inspect cycle counts and the order of the resulting group element.
Try this
Each face turn permutes 54 oriented facelets. Repeat an algorithm until it returns to identity; its order is the least common multiple of its cycle lengths.
Equations used in the module
Equations g^ord(g) = e ord(g) = lcm(lengths of disjoint cycles) [R,U] = R U R⁻¹ U⁻¹ A B and B A need not be equal
