Compound of five cuboctahedra

In geometry, this uniform polyhedron compound is a composition of 5 cuboctahedra. It has icosahedral symmetry I_h.

Compound of five cuboctahedra
Type	Uniform compound
Index	UC59
Polyhedra	5 cuboctahedra
Faces	40 triangles, 30 squares
Edges	120
Vertices	60
Symmetry group	icosahedral (Ih)
Subgroup restricting to one constituent	pyritohedral (Th)

Cartesian coordinates

Cartesian coordinates for the vertices of this compound are all the cyclic permutations of

(±2, 0, ±2)

(±τ, ±τ⁻¹, ±(2τ−1))

(±1, ±τ⁻², ±τ²)

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

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.