A Symmetrohedron Featuring Twelve Regular Pentagons, Thirty Regular Octagons, and Twenty Equilateral Triangles

In addition to the sixty-two regular faces, this polyhedron also has two sets of sixty isosceles trapezoids, shown in different shades of blue. That’s 182 faces in all. I made it using Stella 4d, which you can try for free at www.software3d.com/Stella.php.

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 122-Faced Symmetrohedron Featuring Twelve Regular Decagons and Thirty Regular Octagons

I previously blogged a different version of this symmetrohedron, one which sacrifices octagon regularity for regularity of all the other faces. Both polyhedra were created using Stella 4d: Polyhedron Navigator, which you can try for free right here. In this version, the twenty red hexagons are equiangular, and the sixty green faces are isosceles trapezoids.