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.

The Third Stellation of the Rhombic Dodecahedron

The model above shows the rhombic dodecahedron colored with one color per face, unless those faces are parallel. The one below shows this solid in “rainbow color mode.”

I made both of these using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.