Compound of five icosahedra

The compound of five icosahedra is uniform polyhedron compound. It's composed of 5 icosahedra, rotated around a common axis. It has icosahedral symmetry I_h.
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
where τ = /2 is the golden ratio.