Compound of two icosahedra

As a holosnub, it is represented by Schläfli symbol β{3,4} and Coxeter diagram .

The triangles in this compound decompose into two orbits under action of the symmetry group: 16 of the triangles lie in coplanar pairs in octahedral planes, while the other 24 lie in unique planes.

It shares the same vertex arrangement as a nonuniform truncated octahedron, having irregular hexagons alternating with long and short edges.

Together with its convex hull, it represents the icosahedron-first projection of the nonuniform snub tetrahedral antiprism.

Cartesian coordinates for the vertices of this compound are all the permutations of where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

Holosnub octahedron, β{3,4}