A 50-Faced Symmetrohedron with Cuboctahedral Symmetry

This image was created using Stella 4d, software you may try for yourself (for free) at http://www.software3d.com/Stella.php.

In this symmetrohedron, the red, blue, and green faces are regular polygons. Only the yellow isosceles trapezoids are irregular.

Zonohedra Based on the Pentagonal Dipyramid

Here’s a pentagonal dipyramid. It’s one of the Johnson solids.


The polyhedra-manipulation software I use, Stella 4d (available as a free trial download right here), lets the user make zonohedra from various “seed” polyhedra. When I made one with zones based on the vertices of the pentagonal dipyramid, a decagonal prism was the result. This surprised me; I wasn’t expecting to see a familiar polyhedron.

zonohedrified penta dipyramid v

Other selections gave me the results I expected: polar zonohedra I had never seen before. Here’s the one based on the edges of the pentagonal dipyramid.

zonohedrified penta dipyramid e

The next one is based on the pentagonal dipyramid’s faces.

zonohedrified penta dipyramid f

Here’s one based on vertices and edges:

zonohedrified penta dipyramid v e

This next one is based on vertices and faces.

The next one is based on edges and faces.

Finally, here’s the last one, with zones based on the faces, edges, and vertices of a pentagonal dipyramid.