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.

A Compound of Three Elongated Octahedra

This compound is the 16th stellation of the tetrakis hexahedron, the Catalan solid which is the dual of the Archimedean truncated octahedron. I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

Spectral Octahedra

Stella 4d: Polyhedron Navigator has a “put models on vertices” function which I used to build this complex of octahedra. If you’d like to try this software for yourself, there is a free trial version available at http://www.software3d.com/Stella.php.

A Fractured Octahedron

Sometimes, when using Stella 4d (available here) to make various polyhedra, I lose track of how I got from wherever I started to the final step. That happened with this fractured version of an octahedron.

Octahedra and Truncated Cubes Can Fill Space Without Leaving Any Gaps

Augmented Trunc Cube

I created this using Stella 4d, which you can try for free right here. It’s much like a tessellation, but in three dimensions instead of two.

Octahedra and Cuboctahedra Can Fill Space Without Leaving Any Gaps

Augmented Cubocta

I created this image using Stella 4d, which you can try for free right here. It’s much like a tessellation, but in three dimensions instead of two.