title: Compound of dodecahedron and icosahedron
text: # 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.
  
  