Some Enantiomorphic-Pair Compounds

Posted on 3 November 2015 by RobertLovesPi

In the last post here, three different color-versions of the same cluster-polyhedron were shown. Since this cluster-polyhedron is chiral, it is possible to make a compound of it, and its own enantiomer (or “mirror-image,” if you prefer). This first image shows that, with the face-color chosen by the number of sides of each face.

Shown next is the dual of this figure, also colored by the number of sides of each face.

Next, another image of the first compound shown here, but with the colors chosen by face-type (referring to each face’s position in the overall polyhedron).

Finally, here is the dual, again, also with colors chosen by face-type.

All four of these images were generated with Stella 4d, a computer program available at http://www.software3d.com/Stella.php.

Two Different Versions of an Expanded Snub Dodecahedron, Both of Which Feature Regular Decagons

Posted on 18 July 2015 by RobertLovesPi

The snub dodecahedron, one of the Archimedean solids, can be expanded in multiple ways, two of which are shown below. In each of these expanded versions, regular decagons replace each of the twelve regular pentagons of a snub dodecahedron.

Like the snub dodecahedron itself, both of these polyhedra are chiral, and any chiral polyhedron can be used to create a compound of itself and its own mirror-image, Below, you’ll find these enantiomorphic-pair compounds, each made from one of the two polyhedra above, together with its own reflection.

All four of these images were created using Stella 4d: Polyhedron Navigator, software available (including a free trial download) at this website.

Compounds of Enantiamorphic Archimedean Solid Duals

Posted on 19 December 2014 by RobertLovesPi

An enantiomorphic-pair compound requires a chiral polyhedron, for it is a compound of a polyhedron and its mirror image. Among the Archimedeans, only the snub cube and snub dodecahedron are chiral. For this reason, only threir duals are chiral, among the Archimedean duals, also known as the Catalan solids.

That’s a compound of two mirror-image snub cube duals (pentagonal icositetrahedra) above; the similar compound for the snub dodecahedron duals (pentagonal hexacontahedra) is below.