Monthly Archives: December 2014

A Survey of Polyhedra with Pyritohedral Symmetry

The simplest way for many to understand pyritohedral symmetry is simply to realize that it is the symmetry of the seams in a volleyball. The first time I encountered this unusual symmetry-type was in the golden icosahedron I blogged about … Continue reading

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If You Have Enough Platonic Dodecahedra Around, and Glue Them Together Just Right, You Can Make a Rhombic Triacontahedron.

Aren’t you glad to know that? As soon as I found out isocahedra can form a rhombic dodecahedron (see last post), I knew this would be true as well. Why? Zome explains why, actually. It’s at http://www.zometool.com. Anything buildable with … Continue reading

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A Rhombic Dodecahedral Lattice, Made of Icosahedra

I used Stella 4d: Polyhedron Navigator to make this. You can find this program at http://www.software3d.com/Stella.php.

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A Compound of Three Square Dipyramids

The reason I am not calling this a compound of three octahedra is that the faces of the dipyramids aren’t quite equilateral. They are, however, isosceles. This was created with Stella 4d, which you can buy, or try for free, … Continue reading

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Happy Second Anniversary of Your Simulated Existence

The world ended on this day in 2012 — December 21 — when the Mayan calendar began a new cycle. We now secretly live in a computer simulation run by highly advanced ancient Mayan aliens. They have authorized me to … Continue reading

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A Partially-Invisible Rhombicosidodecahedron, and One of Its Stellations

The polyhedron above originally had thirty yellow square faces, but I rendered them invisible so that the interior structure of this polyhedron could be seen. When stellating such a partially-invisible figure, the new faces “inherited” from the “parent polyhedron” are … Continue reading

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The Seven Zonish Dodecahedra with Zones Added Based on Faces, Edges, and/or Vertices

If a zonish dodecahedron is created with zones based on the dodecahedron’s vertices, here is the result. If the same thing is done with edges, this is the result — an edge-distorted version of the great rhombicosidodecahedron. Another option is … Continue reading

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