A Polyhedron Featuring a Dozen Regular Heptagons and a Whole Mess of Quadrilaterals

There are four different shapes of quadrilaterals here, but they have one thing in common: there are twelve of each of them. Add those 48 quads to the twelve regular heptagons, and that gives a total of 60 faces. I found this polyhedron while playing with the snub dodecahedron, using Stella 4d: Polyhedron Navigator, a program you can try for free right here.

In the image below, each of the four types of quadrilateral appears with its own color.

A 32-faced Polyhedron Featuring 4 Regular Heptagons

In addition to the four regular heptagons, this polyhedron has four quadrilateral faces, plus 24 triangles. I made it using Stella 4d, which you can try for free here. The second image, below, shows the same polyhedron from a different angle.

A Polyhedron Featuring Sixty Regular Heptagons

In addition to the sixty heptagons, there are twelve regular pentagons and sixty quadrilaterals in this polyhedron, along with 380 triangles of various shapes and sizes. That’s 512 faces in all.

I used Stella 4d: Polyhedron Navigator to make this. You may try this program, for free, at http://www.software3d.com/Stella.php.