A Dodecahedron, Augmented with Twelve Pentagonal Cupolae

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A Rhombicosidodecahedron, with Twelve Pentagonal Cupolae Excavated

Software credit: I made this using Stella 4d, available at http://www.software3d.com/Stella.php (free trial download available).

The Compound of Five Rhombic Dodecahedra

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The Compound of Five Rhombic Dodecahedra

This compound is unusual in that it is most attractive as a ball-and-stick model, with the faces rendered invisible, rather than the traditional coloring for compounds. In the traditional coloring, no faces are hidden, and each component of the compound is given faces of a different color. Here’s the same compound, rendered in the traditional manner:

RD 5

Of course, matters of aesthetics are not subject to mathematical proof. Some might prefer the second version to the first.

Software credit:  please see www.software3d.com/Stella.php to try or buy Stella 4d, the software I use to make these polyhedral images.

Tessellation Featuring Regular Dodecagons, Regular Octagons, Squares, and Hexaconcave, Equilateral Dodecagons

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Tessellation Featuring Regular Dodecagons, Regular Octagons, Squares, and Hexaconcave. Equilateral Dodecagons