Creating a Polyhedron Featuring 72 Regular Pentagons

This polyhedron contains 72 regular polygons, 20 equilateral triangles, and 302 faces in all. But where did it come from?

I made it, starting with the snub dodecahedron, using Stella 4d (available here).

This is the dual of the snub dodecahedron. It is called the pentagonal hexecontahedron.

There are various ways of combining polyhedra with their duals, and the one I used here is called morphing duals by expansion. Here’s the 50%-morphed version.

The next step was to use Stella’s “try to make faces regular” function, which worked best for the 72 pentagonal faces, as well as the twenty of the equilateral triangles.

From there, simple changes of face-color produced the polyhedron shown at the top of this post.

An Intermediate Form Between the Icosidodecahedron and the Rhombic Triacontahedron

This polyhedron combines the faces of an icosidodecahedron (red and blue) with the those of a rhombic triacontahedron (green). The gaps between those two sets of polygons are the yellow rectangles. I made this using the “morph duals by expansion” function of Stella 4d: Polyhedron Navigator. You can try this program for yourself, free of charge, at http://www.software3d.com/Stella.php.

A Dodecahedron, with Mandalas

The mandala used here first appeared in this blog-post. I then used Stella 4d: Polyhedron Navigator to put those images on the faces of a dodecahedron. If you’d like to try this program yourself, you can do so, for free, at http://www.software3d.com/Stella.php.

A Polyhedron Featuring Six Regular Octagons, Twelve Hexagons, and Twenty-Four Pentagons

I made this polyhedron using Stella 4d: Polyhedron Navigator. If you’d like to give this software a free try, the website to visit is http://www.software3d.com/Stella.php.

A Rhombic Dodecahedron Decorated with Golden Mandalas

To make this, I used Stella 4d: Polyhedron Navigator to take the image I blogged here, and then project it onto the faces of a rhombic dodecahedron. Next, I put that polyhedron into motion for the .gif shown below.

If you’d like to give Stella a free try, the site to visit is http://www.software3d.com/Stella.php.