Geometrical and Topological Analogues of Rubik's Cube

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!

A quick overview of what MagicTile supports:
MagicTile is currently approaching one thousand configured twisty puzzles, with thousands more possible. The homebase for discussion of this program is the 4D_Cubing Yahoo group, and we track solutions on the Superliminal wiki.

The MagicTile code is available on GitHub.

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