@heavyrocks,

I'm a little confused about what you want. In particular, you wrote
I guess the map should really just look like what you see when you rotate a rubik's cube in your hand.
I know of at least two free realtime 3D display programs that can show a perspective view of an object of whatever shape you define, which the player could rotate and view in realtime.

Click image for larger version. 

Name:	cube.jpg 
Views:	1311 
Size:	61.5 KB 
ID:	42050
(it took me about 15 minutes to create this object in my favorite display program, mostly because I kept making typos.)

The programs include programming languages which would allow you to define the motions of the pieces.
e.g. click on piece, rotate playing field, click on destination, check validity