Three Zome Constructions I Made With Students in 2012

Zome can be rearranged in trillions of ways. Here are three of them.

I found these yesterday in Facebook’s “10 years ago” memories it likes to give me every day. If you want to get your own Zome, the website to visit is

Augmenting the Icosidodecahedron With Pyramids

Here’s an icosidodecahedron, one of the thirteen Archimedean solids.

Using a computer program called Stella 4d (available here), I augmented each face of this solid with a pyramid. Here’s the result.

Also interesting is the dual of this pyramid-augmented icosidodecahedron:

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

A Fifty-Faced Polyhedron Featuring Eighteen Regular Octagons

In addition to the eighteen regular octagons, this polyhedron also has eight equiangular hexagons and twenty-four isosceles trapezoids among its fifty faces. I made it using Stella 4d, which you can try, for free, right here.

Repeated Augmentations of a Dodecahedron With More and More Dodecahedra

Here’s a single dodecahedron.

A new “cluster polyhedron” can be made by augmenting each pentagonal face with another dodecahedron.

If you can do it once, you can do it again, augmenting each pentagon with a new dodecahedron.

Once more.

I made these polyhedral clusters using Stella 4d: Polyhedron Navigator, which you can try for free at