Places I Have Been, #3 (Updated for Yellowstone Trip)

My wife Dee and I live in Arkansas, the state shown in yellow above. This map shows, in pink, states we have visited together, between 2013 and the present. I just updated it for our vacation to Yellowstone National Park, which roughly doubled the pink area. States and provinces shown in blue are ones I have visited, but not with Dee, all before 2013. It is my ambition to visit other continents as well — it just hasn’t happened yet.

We took a lot of pictures on our trip, and they’ll show up here soon. First, though, I need sleep, for that was quite a long drive!

A Rhombic Enneacontahedron, Made of Zome

Zome is a ball-and-stick modeling system which can be used to make millions of different polyhedra. If you’d like to get some Zome for yourself, just visit

A Symmetrohedron Featuring Regular Octagons, Pentagons, and Triangles

The only irregular faces in this polyhedron are the quadrilaterals (kites and rectangles). I made it using Stella 4d, which you can try for yourself — for free — at

A Zonohedron Which Is Also a Symmetrohedron

I made this using Stella 4d, which you can try for free at

This zonohedron is based on the icosidodecahedron / rhombic triacontahedron compound — more specifically, on its edges. Twelve faces are regular decagons, twenty are regular hexagons, sixty are squares, and the only irregular faces are the thirty equilateral octagons. That’s 122 faces in all.

A Three-Level Dodecahedron, Together with Its Dual

I made these using Stella 4d, which you can try for yourself, free, at

After I’d posted this, a helpful friend on Facebook told me the official name of the first polyhedron shown here — a pentalofted chamfered dodecahedron.

A Zonish Icosahedron

This zonish polyhedron was made by adding zones based on the faces and vertices of an icosahedron. Its faces are 30 decagons, twenty equilateral triangles, and twelve panels of five rhombi each. I used Stella 4d to create this; it’s a program you can try for free at