Created using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
Created using Stella 4d: Polyhedron Navigator, available here.
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 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.
Software credit: see http://www.software3d.com/stella.php to try or buy Stella 4d, the software I used to create this image.
The triakis tetrahedron is the dual of the truncated tetrahedron.
Software used: see http://www.software3d.com/stella.php.