Compound of dodecahedron and icosahedron
# Compound of dodecahedron and icosahedron

First stellation of icosidodecahedron :

| Type | Dual compound |
| - | - |
| Coxeter diagram | ∪ |
| Stellation core | icosidodecahedron |
| Convex hull | Rhombic triacontahedron |
| Index | $W_{47}$ |
| Polyhedra | 1 icosahedron 1 dodecahedron |
| Faces | 20 triangles 12 pentagons |
| Edges | 60 |
| Vertices | 32 |
| Symmetry group | icosahedral $(I_h)$ |

In geometry, this polyhedron can be seen as either a polyhedral stellation or a compound.

## As a compound

It can be seen as the compound of an icosahedron and dodecahedron. It is one of four compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual.

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

This can be seen as the three-dimensional equivalent of the compound of two pentagons ({10/2} "decagram"); this series continues into the fourth dimension as the compound of 120-cell and 600-cell and into higher dimensions as compounds of hyperbolic tilings.

| A dodecahedron and its dual icosahedron | The intersection of both solids is the icosidodecahedron, and their convex hull is the rhombic triacontahedron. |
| - | - |

## As a stellation

This polyhedron is the first stellation of the icosidodecahedron, and given as Wenninger model index 47.

The stellation facets for construction are:

## In popular culture

In the film Tron (1982), the character Bit took this shape when not speaking.

In the cartoon series Steven Universe (2013-2019), Steven's shield bubble, briefly used in the episode Change Your Mind, had this shape.

