Compound of five cuboctahedra

Last updated
Compound of five cuboctahedra
UC59-5 cuboctahedra.png
Type Uniform compound
IndexUC59
Polyhedra5 cuboctahedra
Faces40 triangles, 30 squares
Edges120
Vertices60
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 Ih. It could also be called the anticosicosahedron.

Contents

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).

Construction

The compound of 5 cuboctahedra could be made by the rectification of the compound of five cubes or compound of five octahedra. It could also be formed by the expansion of the compound of five or ten tetrahedra.

References