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.

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.

A Polyhedron with Isosceles Trapezoids and Regular Pentagons as Faces

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

A Non-Convex, Pyritohedral Dodecahedron with Non-Convex Pentagonal Faces

I created this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php. Starting with the Platonic dodecahedron, I dropped the symmetry of the model down from icosahedral to tetrahedral, then stellated it six times. I also put the resulting polyhedron into “rainbow color mode” before making this .gif image.

Here’s a net for this solid. To build it, you’ll need six copies of this net.