title: Compound of great icosahedron and great stellated dodecahedron
text: # 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 |
  | - | - |
  