Compound of five cuboctahedra
# Compound of five cuboctahedra

Compound of five cuboctahedra :

| Type | Uniform compound |
| - | - |
| Index | $UC_{59}$ |
| Polyhedra | 5 cuboctahedra |
| Faces | 40 triangles, 30 squares |
| Edges | 120 |
| Vertices | 60 |
| Symmetry group | icosahedral $(I_h)$ |
| Subgroup restricting to one constituent | pyritohedral $(T_h)$ |

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, $±τ^{−2},$ $±τ^2)$

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

