The great triakis octahedron is a stellation of the deltoidal icositetrahedron.

In geometry, the great triakis octahedron is the dual of the stellated truncated hexahedron (U).

In geometry, a triakis octahedron is an Archimedean dual solid, or a Catalan solid.

The triakis octahedron is a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane.

If the truncated cube has unit edge length, its dual triakis octahedron has edges of lengths 2 and .

It has the same topology as the convex Catalan solid, the triakis octahedron, which has much shorter pyramids.

Equilateral triakis octahedron (stella octangula)

The triakis octahedron is one of a family of duals to the uniform polyhedra related to the cube and regular octahedron.

A triakis octahedron is a vital element in the plot of cult author Hugh Cook's novel The Wishstone and the Wonderworkers.

In Japan the pattern is called asanoha for hemp leaf, although the name also applies to other triakis shapes like the triakis icosahedron and triakis octahedron.

It is also called the small triakis octahedron, so as to differentiate it from the great triakis octahedron, the dual of the stellated truncated hexahedron.

Because of the existence of this polyhedron, the Catalan solid known as the triakis octahedron is occasionally referred to as the small triakis octahedron.

The triakis tetrahedron is the Kleetope of a tetrahedron, the triakis octahedron is the Kleetope of an octahedron, and the triakis icosahedron is the Kleetope of an icosahedron.

Geometrically, a polyhedron representing the Goldner-Harary graph may be formed by gluing a tetrahedron onto each face of a triangular dipyramid, similarly to the way a triakis octahedron is formed by gluing a tetrahedron onto each face of an octahedron.