Compound of five icosahedra
# Compound of five icosahedra

Compound of five icosahedra :

| Type | Uniform compound |
| - | - |
| Index | $UC_{47}$ |
| Polyhedra | 5 icosahedra |
| Faces | 40+60 Triangles |
| Edges | 150 |
| Vertices | 60 |
| Symmetry group | icosahedral $(I_h)$ |
| Subgroup restricting to one constituent | pyritohedral $(T_h)$ |

The compound of five icosahedra is uniform polyhedron compound. It's composed of 5 icosahedra, rotated around a common axis. It has icosahedral symmetry $I_h.$

The triangles in this compound decompose into two orbits under action of the symmetry group: 40 of the triangles lie in coplanar pairs in icosahedral planes, while the other 60 lie in unique planes.

## Cartesian coordinates

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

    (0, ±2, ±2τ)
    $(±τ^{−1},$ ±1, $±(1+τ^2))$
    (±τ, $±τ^2,$ ±(2τ−1))

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

