Compound of five great icosahedra

This uniform polyhedron compound is a composition of 5 great icosahedra, in the same arrangement as in the compound of 5 icosahedra.

Compound of five great icosahedra
Type	Uniform compound
Index	UC53
Polyhedra	5 great icosahedra
Faces	40+60 Triangles
Edges	150
Vertices	60
Symmetry group	icosahedral (Ih)
Subgroup restricting to one constituent	pyritohedral (Th)

Under the action of the symmetry group, the triangles in this compound decompose into two orbits: 40 of the triangles lie in coplanar pairs in icosahedral planes, while the other 60 lie in unique planes.

References

• Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554.