Compound of five cuboctahedra

Compound of five cuboctahedra
TypeUniform compound
IndexUC59
Polyhedra5 cuboctahedra
Faces40 triangles, 30 squares
Edges120
Vertices60
Symmetry groupicosahedral (Ih)
Subgroup restricting to one constituentpyritohedral (Th)

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

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