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.
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.
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.
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.
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:
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 http://www.software3d.com/Stella.php.
The blue kites have sides which are in the golden ratio (~1.618:1), while the yellow kites’ sides are in a ratio equaling the square of that number, or approximately ~2.618:1.
RobertLovesPi.net 