title: Compound of four hexagonal prisms
text: # Compound of four hexagonal prisms
  
  Compound of four hexagonal prisms :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{38}$ |
  | Polyhedra | 4 hexagonal prisms |
  | Faces | 8 hexagons, 24 squares |
  | Edges | 72 |
  | Vertices | 48 |
  | Symmetry group | octahedral $(O_h)$ |
  | Subgroup restricting to one constituent | 3-fold antiprismatic $(D_{3d})$ |
  
  This uniform polyhedron compound is a symmetric arrangement of 4 hexagonal prisms, aligned with the axes of threefold rotational symmetry of an octahedron.
  
  ## Cartesian coordinates
  
  Cartesian coordinates for the vertices of this compound are all the permutations of
  
      (±1, ±(1−√6), ±(1+√6))
  