The Rhombic Octagonoid, a Zonohedron With Ninety Faces

Posted on 15 February 2020 by RobertLovesPi

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

Posted on 10 December 2019 by RobertLovesPi

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

Posted on 8 December 2019 by RobertLovesPi

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

Posted on 1 June 2019 by RobertLovesPi

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.

Four Zonohedra

Posted on 16 February 2019 by RobertLovesPi

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

Posted on 20 November 2018 by RobertLovesPi

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

Posted on 13 October 2018 by RobertLovesPi

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.