A Platonic/Catalan Compound and Its Dual, a Platonic/Archimedean Compound

Compound of Rhombic Dodeca and Icosa

Shown above: the compound of the icosahedron and the rhombic dodecahedron. Below is its dual, the compound of the dodecahedron and the cuboctahedron.

Compound of Dodeca and Cubocta

Both these compounds were created using the “add/blend polyhedron from memory” function in Stella 4d: Polyhedron Navigator. To check out this program for yourself, just follow this link.

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

If a zonish icosahedron is created with zones based on the icosahedron’s vertices, here is the result.

zonish icosa v

If the same thing is done with edges, this is the result.

zonish icosa e

Another option is faces-only.

zonish icosa f

The next zonish icosahedron has had zones added based on the icosahedron’s faces and edges, both.

zonish icosahedra e f

Here’s the one for vertices and edges.

zonish icosa v e

Here’s the one for faces and vertices.

zonish icosahedron v f

Finally, the last of this set of seven has had zones added based on all three: faces, vertices, and edges.

zonish icosa v e f

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