Three Non-convex Polyhedra with Cuboctahedral Symmetry

These were all created using Stella 4d, a program you can try — for free — at http://www.software3d.com/Stella.php.

A Hybrid of the Snub Dodecahedron and the Truncated Icosahedron

I created this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

Twenty Hexagons and Sixty Pentagons

Created using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

A Hybrid of the Truncated Icosahedron and the Snub Dodecahedron

I made this using Stella 4d: Polyhedron Navigator, a program you can try for free at http://www.software3d.com/Stella.php.

A Snub Dodecahedron Variant

I made this using Stella 4d, which you can try for yourself, for free, at http://www.software3d.com/Stella.php.

A Compound of a Slightly Stretched Truncated Icosahedron and the Rhombic Triacontahedron

Created using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

Sixty Pentagons and Twenty Hexagons

Created using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.

Snub Cube Variant

I stumbled across this while playing with Stella 4d, a program you may try for free at http://www.software3d.com/Stella.php.

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.