Compound of five icosahedraTypeUniform compoundIndexUC47Polyhedra5 icosahedraFaces40+60 TrianglesEdges150Vertices60Symmetry groupicosahedral (Ih)Subgroup restricting to one constituentpyritohedral (Th)
The compound of five icosahedra is uniform polyhedron compound. It's composed of 5 icosahedra, rotated around a common axis. It has icosahedral symmetry Ih.
The triangles in this compound decompose into two orbits under action of the symmetry group: 40 of the triangles lie in coplanar pairs in icosahedral planes, while the other 60 lie in unique planes.
The compound of five icosahedra shares the same vertex arrangement of a nonuniform rhombicosidodecahedron.
Cartesian coordinates Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
(0, ±2, ±2τ) (±τ−1, ±1, ±(1+τ2)) (±τ, ±τ2, ±(2τ−1))
where τ = (1+)/2 is the golden ratio (sometimes written φ).
References .