I’ve done quite a bit on this blog involving modifiying polyhedra via augmentation, in which polyhedra are attached to faces of another polyhedra. This was made using the opposite process, excavation, where parts of a given polyhedron are removed. First, a pentagonal pyramid was excavated from each pentagonal face of the icosidodecahedron. Next, octahedra were excavated from each triangular face. Finally, the bottom face of each of these octahedra was hidden, making it possible to see all the way through this solid. I constructed this with Stella 4d, software you can try or buy at www.software3d.com/Stella.php.

Here’s the same polyhedron again, but with a different color-scheme.