Compound of great icosahedron and great stellated dodecahedron
# Compound of great icosahedron and great stellated dodecahedron

Compound of great icosahedron and stellated dodecahedron :

| Type | stellation and compound |
| - | - |
| Coxeter diagram | ∪ |
| Convex hull | Dodecahedron |
| Polyhedra | 1 great icosahedron 1 great stellated dodecahedron |
| Faces | 20 triangles 12 pentagrams |
| Edges | 60 |
| Vertices | 32 |
| Symmetry group | icosahedral $(I_h)$ |

There are two different compounds of great icosahedron and great stellated dodecahedron: one is a dual compound and a stellation of the great icosidodecahedron, the other is a stellation of the icosidodecahedron.

## Dual compound

It can be seen as a polyhedron compound of a great icosahedron and great stellated dodecahedron. It is one of five compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual. It is a stellation of the great icosidodecahedron.

It has icosahedral symmetry $(I_h)$ and it has the same vertex arrangement as a great rhombic triacontahedron.

This can be seen as one of the two three-dimensional equivalents of the compound of two pentagrams ({10/4} "decagram"); this series continues into the fourth dimension as compounds of star 4-polytopes.

## Stellation of the icosidodecahedron

This polyhedron is a stellation of the icosidodecahedron, and given as Wenninger model index 61. It has the same vertex arrangement as a rhombic triacontahedron, its convex hull.

The stellation facets for construction are:

| Facets from triangle | Facets from pentagon |
| - | - |
