MagicTile is a program that abstracts the Rubik's Cube as a colored regular tiling of squares on the sphere. The familiar "cubeness" is lost, but all the important properties of the original puzzle remain. Once we have a nice analogue of a twist from this perspective, we can consider other colored regular tilings and a huge number of new twisty puzzles become possible, some living in the world of hyperbolic geometry!

http://www.roice3.org/magictile

This program has a dependency on the OpenTK library: https://github.com/opentk/opentk