title: Compound of five cuboctahedra
text: # Compound of five cuboctahedra
  
  Compound of five cuboctahedra :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{59}$ |
  | Polyhedra | 5 cuboctahedra |
  | Faces | 40 triangles, 30 squares |
  | Edges | 120 |
  | Vertices | 60 |
  | Symmetry group | icosahedral $(I_h)$ |
  | Subgroup restricting to one constituent | pyritohedral $(T_h)$ |
  
  In geometry, this uniform polyhedron compound is a composition of 5 cuboctahedra. It has icosahedral symmetry $I_h.$
  
  ## Cartesian coordinates
  
  Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
  
      (±2, 0, ±2)
      (±τ, $±τ^{−1},$ ±(2τ−1))
      (±1, $±τ^{−2},$ $±τ^2)$
  
  where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
  
  