Compound of five great icosahedra
# Compound of five great icosahedra

Compound of five great icosahedra :

| Type | Uniform compound |
| - | - |
| Index | $UC_{53}$ |
| Polyhedra | 5 great icosahedra |
| Faces | 40+60 Triangles |
| Edges | 150 |
| Vertices | 60 |
| Symmetry group | icosahedral $(I_h)$ |
| Subgroup restricting to one constituent | pyritohedral $(T_h)$ |

This uniform polyhedron compound is a composition of 5 great icosahedra, in the same arrangement as in the compound of 5 icosahedra.

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.

