A Dozen Dodecahedra, Surrounding an Icosahedron

I made these virtual models using Stella 4d: Polyhedron Navigator. If you’d like to try this program for yourself — free — the website to visit is http://www.software3d.com/Stella.php.

Two Images of a Toroidal Rhombic Triacontahedron Made of 212 Dodecahedra

I made these using Stella 4d, a program you can try as a free trial download at http://www.software3d.com/Stella.php.

A Twice-Zonohedrified Dodecahedron

If one starts with a dodecahedron, and then creates a zonohedron based on that solid’s vertices, the result is a rhombic enneacontahedron.

If, in turn, one then creates a new zonohedron based on the vertices of this rhombic enneacontahedron, the result is this 1230-faced polyhedron — a twice-zonohedrified dodecahedron. Included in its faces are thirty dodecagons, sixty hexagons, and sixty octagons, all of them equilateral.

Stella 4d: Polyhedron Navigator was used to perform these transformations, and to create the rotating images above. You can try this program for yourself, free, at http://www.software3d.com/Stella.php.

Two Rhombic Polyhedra with Tessellated Faces

These polyhedra are the rhombic dodecahedron (above), and the rhombic triacontahedron (below).

I made both of these using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php. The tessellation on the faces of these polyhedra first appeared right here on this blog, in the post just before this one.

A Three-Level Dodecahedron, Together with Its Dual

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

After I’d posted this, a helpful friend on Facebook told me the official name of the first polyhedron shown here — a pentalofted chamfered dodecahedron.