A Decorated Rhombic Dodecahedron

The patterns on the faces are from the last post here, immediately before this one. I used Stella 4d: Polyhedron Navigator to make this, and you can try this software for free at this website.

Fourteen Heptagrams

The fourteen heptagrams, also known as {7/3} star heptagons, meet at a common vertex in the center of the whole diagram. I did the math using Geometer’s Sketchpad, and then colored the result using MS-Paint.

If I've tried this once, I've tried it at least fifty-five times….

It’s hard to get regular pentagons, regular star pentagons, regular decagons, and related polygons to tessellate the plane while maintaining radial symmetry. This is my latest attempt.

Filling Space with Cuboctahedra and Octahedra

To get started packing space with cuboctahedra and octahedra, I started with a single octahedron, then augmented its square faces with additional cuboctahedra.

Next, I augmented each triangular face with a blue octahedron.

Next, I augmented each square face with a cuboctahedron.

Next, I added still more cuboctahedra.

The next step was to augment the yellow triangular faces with blue octahedra.

I next added more cuboctahedra.

This process may be continued without limit. I used a program called Stella 4d to make these models, and you can try this software yourself, for free, at this website.