Five, Six, Seven

The post immediately before this one features a polyhedron with faces which are all either pentagons, hexagons, or heptagons, and here’s another solid which meets the same criteria. I created it using Stella 4d, which you may try for free at

A Polyhedron with Pentagons, Hexagons, and Heptagons as Faces

This polyhedron has 60 heptagonal faces, 20 faces which are regular hexagons, and 72 pentagonal faces. I made it using Stella 4d, which you can try for free at

Two Non-convex Polyhedra with Cuboctahedral Symmetry

I made both of these while playing around with Stella 4d: Polyhedron Navigator, a program you can try out for free at

A Non-convex, Pyritohedral Dodecahedron with Non-convex Pentagonal Faces

I created this using Stella 4d, which you can try for free at Starting with the Platonic dodecahedron, I dropped the symmetry of the model down from icosahedral to tetrahedral, then stellated it six times. I also put the resulting polyhedron into “rainbow color mode” before making this .gif image.

My 2019 Birthday Star

I was born 51 years ago today. To mark the occasion, here’s a 51-pointed star. It’s made of {17/7} heptadecagrams repeated 3 times, and with their edges extended as lines, in three different colors. This works because 51 = (17)(3).