title: Compound of five stellated truncated hexahedra
text: # Compound of five stellated truncated hexahedra
  
  Compound of five stellated truncated hexahedra :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{58}$ |
  | Polyhedra | 5 stellated truncated hexahedra |
  | Faces | 40 triangles, 30 octagrams |
  | Edges | 180 |
  | Vertices | 120 |
  | Symmetry group | icosahedral $(I_h)$ |
  | Subgroup restricting to one constituent | pyritohedral $(T_h)$ |
  
  This uniform polyhedron compound is a composition of 5 stellated truncated hexahedra, formed by star-truncating each of the cubes in the compound of 5 cubes.
  
  ## Cartesian coordinates
  
  Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
  
      (±(2−√2), ±√2, ±(2−√2))
      (±φ, $±(φ^{−1}−φ^{−1}√2),$ ±(2φ−1−φ√2))
      (±1, $±(φ^{−2}+φ^{−1}√2),$ $±(φ^2−φ√2))$
      (±(1−√2), $±(−φ^{−2}+√2),$ $±(φ^2−√2))$
      (±(φ−φ√2), $±(−φ^{−1}),$ $±(2φ−1−φ^{−1}√2))$
  
  where φ = (1+√5)/2 is the golden ratio.
  
  