title: Compound of twenty octahedra
text: # Compound of twenty octahedra
  
  Compound of twenty octahedra :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{14}$ |
  | Polyhedra | 20 octahedra |
  | Faces | 40+120 triangles |
  | Edges | 240 |
  | Vertices | 60 |
  | Symmetry group | icosahedral $(I_h)$ |
  | Subgroup restricting to one constituent | 6-fold improper rotation $(S_6)$ |
  
  The compound of twenty octahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 20 octahedra (considered as triangular antiprisms). It is a special case of the compound of 20 octahedra with rotational freedom, in which pairs of octahedral vertices coincide.
  
  ## Related polyhedra
  
  This compound shares its edge arrangement with the great dirhombicosidodecahedron, the great disnub dirhombidodecahedron, and the compound of twenty tetrahemihexahedra.
  
  It may be constructed as the exclusive or of the two enantiomorphs of the great snub dodecicosidodecahedron.
  
  | Convex hull | Great snub dodecicosidodecahedron | Great dirhombicosidodecahedron |
  | - | - | - |
  | Great disnub dirhombidodecahedron | Compound of twenty octahedra | Compound of twenty tetrahemihexahedra |
  