Three Variations of Kepler’s Stella Octangula

The Stella Octangula was the name Johannes Kepler gave, centuries ago, to the compound of two tetrahedra. Here are three variations on it, all created using Stella 4d, a program you may try at

stella octangular variantstella octangular variant anotherstella octangular variant third

The Hyperspace Analogue of the Stella Octangula

The simplest polyhedron is the tetrahedron, and it is self-dual. The compound of two tetrahedra puts these duals together, and is most often called the Stella Octangula, a name Johannes Kepler gave it in the early 17th Century.


In hyperspace, or 4-space, the simplest polychoron is the pentachoron, or 5-cell. Like the tetrahedron in 3-space, it is also self-dual. Here is the compound of two of them: hyperspace’s version of the Stella Octangula.

Compound of 1-Pen, 5-cell, Pentachoron and dual

Website to find the software used to make these images: