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 Tessellation Featuring Regular Octagons and Triangles, Together with Equilateral Four- and Six-Pointed Stars

This tessellation started with a single equilateral triangle, surrounded by regular octagons. The one shown below is the same tessellation, but with different colors.

A Tessellation Featuring Regular Heptagons and Triangles, Together with Equilateral Four- and Six-Pointed Stars

This started with the idea of attaching a regular heptagon to each side of an equilateral triangle. From there, it took on a life of its own.

Here’s another version, with different colors:

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.