Four Octahedra

There’s a tetrahedron in the center of this figure, but you can’t see it because it is covered on all sides by octahedra. I made this using Stella 4d, which you can try for free at this website.

Here’s another version, with a different coloring-scheme.

Augmenting, then Reaugmenting, the Octahedron

The blue figure above is an octahedron. The next image shows what happens if red octahedra are used to augment each of the blue octahedron’s faces.

The third image shows what happens if yellow octahedra are used to augment each red face in the second figure.

These polyhedral images were created using Stella 4d: Polyhedron Navigator, which you can try for free at

An Octahedron Made of Lux Blox

This is the first model I built with Lux Blox, a modeling-system I’ve been checking out. If you’d like to try Lux for yourself, the website to visit to get them is

lux octahedron 3

This is an octahedron with an edge length of two. The eight triangular faces are blue, while the edges of the octahedron are orange. Apart from their colors, all these pieces are identical — the basic Lux block, also known as a Lux square. With just this one block, you can build literally millions of things. I’m into polyhedra, so that’s what I’ll be building a lot of, but someone obsessed with dinosaurs could build models of those, as well. Lux Blox are that versatile.

Lux octahedron 2

The images above and below show the same Lux polyhedron, viewed from different angles.

Lux octahedron 1

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

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

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.