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 Faceting of the Rhombcuboctahedron

Faceted Rhombicubocta

This particular faceting of the rhombcuboctahedron can also be viewed as a cluster of stella octangulae. I made it using Stella 4d, polyhedron-manipulating software you can try, for yourself, at http://www.software3d.com/Stella.php.

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 http://www.software3d.com/Stella.php.

stella octangular variantstella octangular variant anotherstella octangular variant third

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 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.

A Bizarre Variant of the Stella Octangula

Image

A Bizarre Variant of the Stella Octangula

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.