Fun article! Makes me want to play with prolog again.

I put together something looking at a rubik's cube as a permutation of numbers a while back. https://taeric.github.io/cube-permutations-1.html I remember realizing that my representation essentially had some permutations of numbers that it would never hit, but wasn't sure it was worth trying to more directly model the pieces of the cube. Curious if there are advantages here that I'm ignoring.

one nice thing is that if you represent the state as a permutation matrix P, and have a matrix of starting piece locations x, rendering is just Px. Then, for smooth rotation animations, if your move is a permutation M, animation is just expm ( t logm( M)) P x with t going from 0 to 1

I blather about the permutation matrix of a rubiks cube for a long while at https://www.hgreer.com/TwistyPuzzle/