Compound of the Tetrahedron and the Triakis Tetrahedron

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Compound of the Tetrahedron and the Triakis Tetrahedron

The triakis tetrahedron is the dual of the truncated tetrahedron.

Software used: see http://www.software3d.com/stella.php.

The Compound of Five Tetrahedra

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The Compound of Five Tetrahedra What would happen if each face in this compound were to be augmented by an octahedron of the same color? To find out, just see the next post!

I produced this image using Stella 4d, software you can find at www.software3d.com/Stella.php.

The Hyperspace Analogue of the Stella Octangula

Posted on 7 February 2013 by RobertLovesPi

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.