A Polyhedron With Sixty Isosceles Trapezoids and Twelve Regular Pentagons as Faces

The polyhedron above is the convex hull of the pyramid-augmented snub dodecahedron seen in the last post. The one below is its dual, and its faces are sixty kites, and twenty equilateral triangles.

I made these using Stella 4d, which you can try for free right here.

A Snub Dodecahedron, Augmented With Pyramids

I made this using Stella 4d, which you can try for free right here.

A Compound of Five Tetrahedra and One Small Stellated Dodecahedron

I made this using Stella 4d, a program you can try for free right here.

A Tetrahedron Variant

I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

Starfish III

Image

Augmenting the Truncated Icosahedron

Here’s a truncated icosahedron, one of the thirteen Archimedean solids.

The next image shows this solid with its hexagonal faces augmented by prisms.

This augmented polyhedron has an interesting dual:

Finally, here’s this dual shown in “rainbow color mode.”

These images were created with Stella 4d, a program you can try for free right here.

Compound of Two Stellated Polyhedra

The yellow component of this compound is the small stellated dodecahedron. As for the blue component, I’m not sure what it’s called. I made this using Stella 4d, which you can try for free right here.

A Twisted and Stellated Polyhedron

I stumbled upon this polyhedron while doing a “random walk” session with Stella 4d: Polyhedron Navigator. If you’d like to try this program for free, you can get a free trial download at this website.

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 http://www.zometool.com.

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: