A Fifty-faced Zonohedron Which Is Also a Symmetrohedron

I created this symmetrohedron as the zonohedron based on the faces, edges, and vertices of the tetrahedron. It has fifty faces: thirty squares, plus eight regular hexagons, and twelve merely-equilateral hexagons. I made it using Stella 4d, which you can try for free at this website.

A Zonohedron Based on the Vertices of a Snub Cube

This zonohedron has 432 faces, and is shown here with two different coloring-schemes — coloring faces by number of sides (above) and rainbow color mode (below). I made these using Stella 4d, which you can try for yourself, for free, at this website: http://www.software3d.com/Stella.php.

A Zonohedron with 1,410 Faces

This version colors the faces by number of sides.

This one is in “rainbow color mode.”

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

A 50-Faced Symmetrohedron Which Is Also a Zonohedron

I made this polyhedron by creating a zonohedron based on the edges and faces of the truncated tetrahedron. Only the blue hexagons are irregular. Stella 4d was used in its creation, and you may try this program for free at http://www.software3d.com/Stella.php.

A Symmetrohedron Which Is Also a Zonohedron

I made this by zonohedrificaton of an octahedron, using its faces, edges, and vertices, and software called Stella 4d, which you can try for free right here.

This polyhedron has six regular octagons (red), a dozen octagons which are merely equilateral (yellow), eight regular hexagons, and 24 squares.

The Rhombic Octagonoid, a Zonohedron With Ninety Faces

To make this zonohedron with Stella 4d (available as a free trial download here), start with a dodecahedron, and then perform a zonohedrification based on both faces and vertices. It is similar to the rhombic enneacontahedron, with thirty equilateral octagons replacing the thirty narrow rhombic faces of that polyhedron.

I’ve run into this polyhedron from time to time, and have also had students make it. It is the largest zonohedron which can be built using only red and yellow Zome (available here) of a single strut-length (short, medium, or long). I thought it needed a name, so I made one up.

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.