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.

# Tag Archives: zonohedra

# A Zonohedron with 170 Faces

This zonohedron was made using the edges and vertices of the truncated tetrahedron.

I made this using *Stella 4d: Polyhedron Navigator*, which you can try for free right here.

# 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 I’ve also had students make it. It is the largest zonohedron which can be built using only red and yellow Zome (available here). 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.

# Two Views of a Zonohedron with 3690 Faces

I used *Stella 4d* to make these images. You can try this program as a free trial download at http://www.software3d.com/Stella.php.

# A Zonohedron Which Is Also a Symmetrohedron

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.

# Four Zonohedra

To build these zonohedra, I used *Stella4d*, a program you may try for free at http://www.software3d.com/Stella.php.

# Thirteen Zonohedra with Cuboctahedral Symmetry

You can make these images larger by clicking on them.

These were all created using *Stella 4d*, which you can try for free right here.

# 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.

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

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

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