title: Compound of four octahedra
text: # Compound of four octahedra
  
  Compound of four octahedra :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{12}$ |
  | Convex hull | Nonuniform truncated cube |
  | Polyhedra | 4 octahedra |
  | Faces | 8+24 triangles |
  | Edges | 48 |
  | Vertices | 24 |
  | Symmetry group | octahedral $(O_h)$ |
  | Subgroup restricting to one constituent | 3-fold antiprismatic $(D_{3d})$ |
  
  The compound of four octahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 4 octahedra, considered as triangular antiprisms. It can be constructed by superimposing four identical octahedra, and then rotating each by 60 degrees about a separate axis (that passes through the centres of two opposite octahedral faces).
  
  Its dual is the compound of four cubes.
  
  ## Cartesian coordinates
  
  Cartesian coordinates for the vertices of this compound are all the permutations of
  
      (±2, ±1, ±2)
  