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.

The Third Stellation of the Pentagonal Icositetrahedron Is a Compound of Two Irregular Dodecahedra

Here’s the pentagonal icositetrahedron. It is the dual of the snub cube.

And here is its third stellation. As you can see, it’s a compound of two irregular dodecahedra.

I made these images using Stella 4d: Polyhedron Navigator. You can try this program 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.