tetrakis hexahedron

Thus, the compound can be seen as a stellation of the tetrakis hexahedron.

In geometry, a tetrakis hexahedron (also known as a tetrahexahedron) is a Catalan solid.

Polyhedral dice shaped like the tetrakis hexahedron are occasionally used by gamers.

This polyhedron can be confused with a slightly smaller Catalan solid, the tetrakis hexahedron, which has only 24 triangles, 32 edges, and 14 vertices.

As diamond's crystal structure has a cubic arrangement of the atoms, they have many facets that belong to a cube, octahedron, rhombicosidodecahedron, tetrakis hexahedron or disdyakis dodecahedron.

The intersection of the three octahedra is a convex polyhedron with 14 vertices and 24 faces, a tetrakis hexahedron, formed by attaching a low square pyramid to each face of the central cube.

A 24-cell viewed under a vertex-first perspective projection has a surface topology of a tetrakis hexahedron and the geometric proportions of the rhombic dodecahedron, with the rhombic faces divided into two triangles.

A different form of the tetrakis hexahedron, formed by using taller pyramids on each face of the cube, is non-convex but has equilateral triangle faces that again lie on the same planes as the faces of the three octahedra; it is another of the known isohedral deltahedra.

The tetrakis hexahedron is the Kleetope of the cube, formed by adding a square pyramid to each of its faces, and the pentakis dodecahedron is the Kleetope of the dodecahedron, formed by adding a pentagonal pyramid to each face of the dodecahedron.

A fourth isohedral deltahedron with the same face planes, also a stellation of the compound of three octahedra, has the same combinatorial structure as the tetrakis hexahedron but with the cube faces dented inwards into intersecting pyramids rather than attaching the pyramids to the exterior of the cube.