Updating my previous comment - the picture for this was the three-layer cube, not the two-layer, so I got confused. This one is fun, but a little loose, and not as fun as the three-layer.

One of my favorite cubes. If you can solve a tangram cube, this is the same mechanism. It's just involved enough to require a little thought, but it requires only one algorithm, the cuboid corner swap.

Very cool, good turns and beautiful