Five, Six, Seven

The post immediately before this one features a polyhedron with faces which are all either pentagons, hexagons, or heptagons, and here’s another solid which meets the same criteria. I created it using Stella 4d, which you may try for free at http://www.software3d.com/Stella.php.

A Polyhedron with Pentagons, Hexagons, and Heptagons as Faces

This polyhedron has 60 heptagonal faces, 20 faces which are regular hexagons, and 72 pentagonal faces. I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

Two Non-convex Polyhedra with Cuboctahedral Symmetry

I made both of these while playing around with Stella 4d: Polyhedron Navigator, a program you can try out for free at http://www.software3d.com/Stella.php.