Rubik’s abstract polytopes

The well-known puzzle Rubik’s Cube can be generalized in a number of ways, for example by turning it into a 4×4×4 or 5×5×5 puzzle. Alternatively, one may try to generalize the 3×3×3 version of the puzzle to one of the other Platonic solids: the tetrahedron, the octahedron, the dodecahedron, or the icosahedron, as shown in the picture above.