This program by Andrey Astrelin supports large variety of twisty puzzles in higher dimensional spaces.

http://superliminal.com/andrey/mpu/

This is an attempt at modernising the DirectX usage from DirectX3.5 to SharpDX. However, there are still some major errors, as I have not been able to use SharpDX.Toolkit. Perhaps someone with more knowledge of DirectX could help finish the job?