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.

A Zonohedron Which Is Also a Symmetrohedron

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

This zonohedron is based on the icosidodecahedron / rhombic triacontahedron compound — more specifically, on its edges. Twelve faces are regular decagons, twenty are regular hexagons, sixty are squares, and the only irregular faces are the thirty equilateral octagons. That’s 122 faces in all.

A Zonohedron with 1382 Faces, Based on the Rhombicosidodecahedron

This zonohedron was formed from zones based on the faces, edges, and vertices of a rhombicosidodecahedron. The first image shows it colored by face type.

Zonohedrified Rhombicosidodeca 1382 faces by face type

The second image has the faces colored by number of sides.

Zonohedrified Rhombicosidodeca 1382 faces bynumber of sides per face.gif

Finally, here’s one in “rainbow color mode.”

Zonohedrified Rhombis rainbow.gif

These images were all formed using Stella 4d: Polyhedron Navigator, which you can try for free right here.

A Zonohedron Featuring Hexadecagons

Zonohedrified Trunc Octa v e f.gif

I stumbled upon this zonohedron by adding zones to a truncated octahedron, based on its faces, edges, and vertices. It was created using Stella 4d, which you may try for free at http://www.software3d.com/Stella.php. To the best of my recollection, this is the only zonohedron I have seen which includes rhombi, hexagons, octagons, and, of course, the red hexadecagons.