Created using *Stella 4d*, which you can try for yourself, for free, at http://www.software3d.com/Stella.

# Tag Archives: polyhedral

# Twenty Rhombicosidodecahedra Surrounding a Central Icosahedron

# A Compound of a Slightly Stretched Truncated Icosahedron and the Rhombic Triacontahedron

## A Compound of a Slightly-Truncated Icosahedron and the Rhombic Triacontahedron

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# The Eleventh Stellation of the Truncated Octahedron Is an Interesting Polyhedral Compound

This compound has three parts: two tetrahedra, plus one smaller cube. I made it using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.

# Augmenting, and Then Reaugmenting, the Icosahedron, with Icosahedra

A reader of this blog, in a comment on the last post here, asked what would happen if each face of an icosahedron were augmented by another icosahedron. I was also asked what the convex hull of such an icosahedron-cluster would be. Here are pictures which answer both questions, in order.

While the icosahedron augmented by twenty icosahedron forms an unusual non-convex shape, its convex hull is simply a slightly “stretched” version of the truncated dodecahedron, one of the Archimedean solids.

The reader who asked these questions did not ask what would happen if the icosahedron-cluster above were to be augmented, on every face, by yet more icosahedra. However, I got curious about this, myself, and created the answer: the following cluster of even-more numerous icosahedra. This could be called, I suppose, the “reaugmented” icosahedron.

Finally, here is the convex hull of this even-larger cluster. No one asked for it; I simply got curious.

To accomplish the polyhedron-manipulation and image-creation for this post, I used a program called *Stella 4d: Polyhedron Navigator*, which is available at http://www.software3d.com/Stella.php. A free trial download is available there, so you can try the software before deciding whether or not to purchase it.

# The Compound of the Octahedron and the Small Stellated Dodecahedron

I made this rotating virtual model using *Stella 4d: Polyhedron Navigator*, which you can try for yourself at http://www.software3d.com/Stella.php. This solid is different from most two-part polyhedral compounds because an unusually high fraction of one polyhedron, the yellow octahedron, is hidden inside the compound’s other component.