An Expanded Version of the Snub Cube

prism-expanded snub cube convex hull after TTMFR

To make this polyhedron, I started with a snub cube. Next, I augmented all triangular faces of it with prisms, then took the convex hull of the result. Finally, I used Stella 4d‘s “try to make faces regular” function on the convex hull.

Stella 4d: Polyhedron Navigator has a free trial download available here.

The Compound of Five Cubes, Augmented with Thirty Snub Cubes: Three Versions

Cubes 5 augmented by 30 snub cubes

This cluster-polyhedron was made with Stella 4d, software you can try at this website. Above, it is colored by face-type, referring to each face’s position within the overall cluster. In the image below, the original compound of five cubes contained one cube each, of five colors, and then each snub cube “inherited” its color from the cube to which it was attached.

Cubes 5

In the next version, the colors are chosen by the number of sides of each face.

Cubes 5

An Attempt to Blend Five Snub Cubes with One Snub Dodecahedron

snubby

Viewers will be the judges of how successful this attempt to blend these polyhedra actually is. I made it using Stella 4d, software you can try right here.

One Faceting, Each, of the Snub Cube and Snub Dodecahedron

Faceted snub cube

These are facetings of the snub cube (above) and snub dodecahedron (below). I made both using Stella 4d, software you can try for yourself right here.

faceted Snub Dodeca

Compounds of Enantiamorphic Archimedean Solid Duals

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.

Compound of enantiomorphic pair snub cube duals

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.

Compound of enantiomorphic pair

Both these compounds were made with Stella 4d, which is available at http://www.software3d.com/Stella.php.