This uniform polyhedron compound is a composition of 2 icosahedra. It has octahedral symmetry O<sub>h</sub>. As a holosnub, it is represented by Schläfli symbol ò{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.
The icosahedron, as a uniform snub tetrahedron, is similar to these snub-pair compounds: compound of two snub cubes and compound of two snub dodecahedra.
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 ÃÂ = (1+)/2 is the golden ratio (sometimes written ÃÂ).
The dual compound has two dodecahedra as pyritohedra in dual positions: