An Icosahedron, Augmented by Snub Dodecahedra, Plus Two Versions of a Related Polyhedral Cluster

Posted on 12 October 2015 by RobertLovesPi

Because the snub dodecahedron is chiral, the polyhedral cluster, above, is also chiral, as only one enantiomer of the snub dodecahedron was used when augmenting the single icosahedron, which is hidden at the center of the cluster.

As is the case with all chiral polyhedra, this cluster can be used to make a compound of itself, and its own enantiomer (or “mirror-image”):

The image above uses the same coloring-scheme as the first image shown in this post. If, however, the two enantiomorphic components are each given a different overall color, this second cluster looks quite different:

All three of these virtual models were created using Stella 4d, software available at this website.

A Pentagonal Icositetrahedron, Decorated with Rippled Tessellations, Along with Its Compound with Its Own Mirror-Image

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A Pentagonal Icositetrahedron, Decorated with Rippled Tessellations

The decorations on each face were created using the design, made using Geometer’s Sketchpad and MS_Paint, from this post: https://robertlovespi.wordpress.com/2014/05/28/rippling-tessellation-using-squares-regular-octagons-and-octaconcave-equilateral-hexadecagons/. I then used Stella 4d, available at http://www.software3d.com/Stella.php, to project this flat image onto each face of this chiral polyhedron, the dual of the snub cube, and make this rotating image.

Next, I used Stella to add this figure to its own mirror-image, to make a compound — something that is always possible with chiral polyhedra. Here is the result.

A Cube of Snub Cubes

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A Cube of Snub Cubes

This cubic arrangement of eight snub cubes, one of the minority of polyhedra which are chiral, includes four “right-handed” snub cubes, and four that are “left-handed.”

Stella 4d was used to create this image, and you may try it for free at http://www.software3d.com/Stella.php.

An Enantiomorphic Pair of Snub Cubes

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An Enantiomorphic Pair of Snub Cubes

Unlike most polyhedra, the snub cube is chiral, meaning it exists in “left-handed” and “right-handed” forms. In this fused pair of snub cubes, there is one of each type.

Stella 4d was used to create this image, and you may try it for free at http://www.software3d.com/stella.php.