## A Bizarre Variant of the Stella Octangula

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The Stella Octangula is another name for the compound of two tetrahedra. In this variant, each triangular face is replaced by a panel of three irregular pentagons. I used Stella 4d to make it, and you can find that program at http://www.software3d.com/Stella.php.

## An Elongated Stella Octangula

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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.

## A Variant of Kepler’s Stella Octangula

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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.

Software credit: see http://www.software3d.com/stella.php to try or buy Stella 4d, the software I used to create this image.

## A Twisted Version of the Stella Octangula

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For comparison, here’s the non-twisted, traditional Stella Octangula:

Software credit: http://www.software3d.com/stella.php

# 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.

Website to find the software used to make these images:  www.software3d.com/stella.php