Tony Fisher Cube
The Tony Fisher cube was created by the man of the same name. Search around and you can find a whole load of strange things that he has done to modify cubes.
You can get these at Meffert's along with a few other modifications and creations by Tony Fisher.
When mixed up, the puzzle changes shape. It is still a cube though and can pretty much be solved like one. When you have the cube solved, you may have some twisted centres. Untwist them as you would for a mastermorphix.