Compound of five cuboctahedra

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)

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

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.