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This uniform polyhedron compound is a composition of 2 icosahedra. It has octahedral symmetry Oh. As a holosnub, it is represented by Schläfli symbol β{3,4} and Coxeter diagram .
Contents
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.
Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the permutations of
(±1, 0, ±τ)where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
Compound of two dodecahedra
The dual compound has two dodecahedra as pyritohedrons in dual positions: