There are radio buttons that select from among eight sub-problems that progress through levels of difficulty, culminating in the full cube.
The 3-d graphics aspects of the implementation were interesting - I wrote an alternative "change camera position" function that suits the symmetry of the Rubik's cube better than the default one in THREE.js. It was very interesting implementing mouse-based face selection and movement in the presence of a perspective projection.
I added a "Record/Rewind" feature, which is in fact a big hint on the key idea for solving the cube: commutators. (If two top pieces are similarly wrong, fix one of them and record the fix. Then, move the other one to where the first one was, and "rewind" your fix!)
Future ideas: 1 - add a scroll bar so that users can explore solutions one move at a time, and go backward and forward.
2 - add links to a text-based web page with hints and suggestions.
3 - add more intermediate sub-problems, with "scramble" options. I.e., have a sub-problem with only the top face and one corner cubie out of place. Have the "scramble" put that one cubie somewhere else, but leave the rest of the top level in place.
4 - HN: any other fun thoughts, suggestions, or ideas?