This project formalizes the Rubik's cube group as a product of corner orientation, corner permutation, edge orientation, and edge permutation.
The solvable subgroup is defined as the the set of positions where both orientations sum to 0 and the permutations have the same sign.
This project includes a widget to visualize elements of the group as physical puzzle states.
For example:
#html (R U R' U' R' F R2 U' R' U' R U R' F').to_html
produces
