Spectral Tetrahedra

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

Five Variants of the Compound of Two Tetrahedra

This is the compound of two tetrahedra, also known as Johannes Kepler’s Stella Octangula.

I found the five variations of this polyhedral compound shown below, located deep within the stellation-series of the great rhombicuboctahedron.

These .gif images were all made using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.

A Tetrahedral Array of Pulsating Tetrahedra

Unnamed.gif

I created this using Stella 4d: Polyhedron Navigator. You may try this software, for free, at http://www.software3d.com/Stella.php.

The Eleventh Stellation of the Truncated Octahedron Is an Interesting Polyhedral Compound

This compound has three parts: two tetrahedra, plus one smaller cube. I made it using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.

Some Variants of Kepler’s Stella Octangula

The Stella Octangula is also known as the compound of two tetrahedra, which works well because the tetrahedron is self-dual. All of these are also two-part compounds, with varying amounts of similarity to the Stella Octangula. The first one is also the 26th stellation of the triakis octahedron, one of the Catalan solids.

compound and 26th stellation of triakis octahedron

All of these were made using Stella 4d, which may be tried or purchased at http://www.software3d.com/Stella.php.

odd compound

SO var d

SO var sdd

SO variant

Two Compounds of Six Tetrahedra Each

compound of six elongated tetrahedra

In the image above, which I stumbled upon using Stella 4d (available here), the tetrahedra are elongated. If they are regular, instead, the same arrangement looks very different:

Tetrahedra 6

Two Colorings of a Hollow Stella Octangula

hollow stella octangula 2

hollow stella octangula

Both of these versions of the stella octangula, or compound of two tetrahedra, were made with Stella 4d, software available at http://www.software3d.com/Stella.php.