A Two-part Polyhedral Compound, Together With Its Dual

I stumbled across this while playing around with Stella 4d, a program you can try for free right here. The red component is the rhombic triacontahedron, while the yellow component is a slightly-stretched version of the strombic hexecontahedron. The dual of this compound is shown below.

A Zome Model of the Compound of the Icosidodecahedron and Its Dual, the Rhombic Triacontahedron

The polyhedral compound above contains an icosidodecahedron (blue) and a rhombic triacontahedron (red). In this compound, the icosidodecahedron’s edges are bisected, while the rhombic triacontahedron’s edges are split into segments with lengths in the square of the golden ratio (~2.618 to 1).

If you want Zome of your own, the place to buy it is http://www.zometool.com.

Playing with One of Stella’s “Morph Duals” Functions

“Morph Duals By Tilting To Duals” is a Stella 4d feature that I haven’t used much. Here’s what happens if you apply it to an icosahedron, at the 50% morphing level: you get the compound of the icosahedron and its dual, the dodecahedron,

If you apply this same operation a second time, here’s what you get.

This appears to be a three-part compound, with two familiar components: the icosahedron (red) and the dodecahedron (orange). Remove those two components, and you get this:

Since this reminds me of an icosidodecahedron, I colored its faces to better suit that identity.

Little peeks at the edges of the solid above made me suspicious, so I hid these purple and green faces, to see the inner structure. Here’s the result.

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

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 http://www.software3d.com/Stella.php.

The Sixth Stellation of the Triakis Octahedron Is a Three-Part Polyhedral Compound

The components of this compound are eight-faced trapezohedra. Here’s what just one of them looks like:

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