The polyhedron above is a compound of twenty cubes and twenty octahedra, colored by symmetry-based face-type. If the same compound is viewed in “rainbow color mode,” it looks like this:
With this particular compound, though, there are two versions — without taking coloring into consideration at all. The other version simply has the twenty cubes and twenty octahedron in a different, but still symmetrical, arrangement:
The compound above uses this second arrangement, colored by face type, and the next image is the same (second) compound, but in “rainbow color mode.”
These rotating polyhedral images were made with Stella 4d, software you can try for yourself, right here.