title: Compound of four triangular prisms
text: # Compound of four triangular prisms
  
  Compound of four triangular prisms :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{30}$ |
  | Polyhedra | 4 triangular prisms |
  | Faces | 8 triangles, 12 squares |
  | Edges | 36 |
  | Vertices | 24 |
  | Symmetry group | chiral octahedral (O) |
  | Subgroup restricting to one constituent | 3-fold dihedral $(D_3)$ |
  
  This uniform polyhedron compound is a chiral symmetric arrangement of 4 triangular prisms, aligned with the axes of three-fold rotational symmetry of an octahedron.
  
  ## Cartesian coordinates
  
  Cartesian coordinates for the vertices of this compound are all the even permutations of
  
      (±1, ±(1+√2), ±(1−√2))
  
  with an even number of minuses in the '±' choices, together with all the odd permutations with an odd number of minuses in the '±' choices.
  
  