The Sixth Stellation of the Triakis Octahedron


The Sixth Stellation of the Triakis Octahedron

The triakis octahedron, a Catalan solid, is the dual of the truncated cube. When stellated six times, the triakis octahedron yields this polyhedral compound with three parts. The parts themselves appear to be unusual, irregular, dipolar octahedra with eight kites for faces, each in sets of four, with their smallest angles meeting at one vertex. However, given that these vertices are, in each case, hidden under the other parts of the compound, there is uncertainty in this.

(Image created with Stella 4d — software you can try yourself at

A Variant of Kepler’s Stella Octangula


A Variant of Kepler's Stella Octangula

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 to try or buy Stella 4d, the software I used to create this image.