The three images below appear smaller than the one above, at first, but can be enlarged with a single click.

These were all created using Stella 4d: Polyhedron Navigator. You can try or buy this software at http://www.software3d.com/Stella.php.

In case you’re wondering, I’m simply calling these polyhedron-inspired images, rather than actual polyhedra, because of the holes in most of them. With the software I use to make these, creating these empty spaces is simply a matter of selecting faces, and then hiding them from view.

For this last one, just for fun, I made the vertices visible — even those where hidden faces touch. The idea was to create a snow-like effect.