I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with those of my employer, nor any other organization, nor institution, of any kind.

# Four Polyhedra Derived From the Icosidodecahedron

I created these using Stella 4d, which you can try for free at this website.

# A Symmetrohedron Derived From the Great Rhombicosidodecahedron

This solid has all the faces of the great rhombicosidodecahedron, plus 120 scalene triangles. I made it using Stella 4d, which you can try for free right here.

# Kepler’s “Stella Octangula,” With Ten Variants

Here’s Johonnes Kepler’s Stella Octangula — also known as the compound of two tetrahedra.

What follows are ten variants of this solid, all made using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.

# Regular Octadecagons As Faces of Symmetrohedra

I tried to make a symmetrohedron using regular octadecagons and regular decagons, but that combination forces the octadecagons to overlap, and that causes the would-be symmetrohedron to be non-convex.

I tried to augment these octadecagons with antiprisms, and then form the convex hull of the result. Here’s what I found:

# A Face-Based Zonohedrified Rhombic Enneacontahedron

The decagons and octagons in this zonohedron are regular. The octadecagons are, sadly, only equilateral. I made this using Stella 4d, which you can try for free, right here.