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.
The Stella Octangula is another name for the compound of two tetrahedra. I made this elongated version, which uses narrow isosceles triangles in place of the usual equilateral triangles, using Stella 4d — polyhedron-manipulation software you can find at http://www.software3d.com/Stella.php.
Johannes Kepler named the compound of two tetrahedra the “stella octangula,” thus helping make it one of the best-known polyhedral compounds today. This variant uses triakis tetrahedra in place of the Platonic tetrahedra in that compound. The triakis tetrahedron is a Catalan solid, and is dual to the truncated tetrahedron.
This is a 600-cell, one of the regular polychora (four-dimensional polytopes), with its edges and vertices rendered invisible, and its cells shrunk so that they do not touch. It’s rotating in hyperspace, and what you are seeing at any given moment is a particular three-dimensional “shadow,” or projection, of the entire figure.
It’s easy to make this sort of thing with software called Stella 4d, written by an Australian friend of mine. Here’s a link to a site where you can try it, as a free trial download, before deciding whether or not to purchase the fully-functioning version: http://www.software3d.com/Stella.php.
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.