These are realised in a networked architecture as well for storing time records (hall of fame) purposes and so on (and perhaps one can come up with some related multi-player game versions later on). Here Loyds' 15 sliding puzzles and Rubik cube variants will be presented.

(Here screenshot showing GUI in action, how to specify area to be rotated etc. will appear in the future.)

One has got to restrict oneself to subgroups of the full group making the problem interesting to solve. And you are invited to study the graphs in the section called “Reticulated 3x3 Cube Variants” resulting from such moves. See the section called “Morphing Group” for a group theoretical treatment (involving the famous group M12) and Chapter 6, Engines for a sophisticated auto solver using that maths (ok, it's mostly vaporware so far).