title: Compound of cube and octahedron
text: # Compound of cube and octahedron
  
  Compound of cube and octahedron :
  
  | Type | Compound |
  | - | - |
  | Coxeter diagram | ∪ |
  | Stellation core | cuboctahedron |
  | Convex hull | Rhombic dodecahedron |
  | Index | $W_{43}$ |
  | Polyhedra | 1 octahedron 1 cube |
  | Faces | 8 triangles 6 squares |
  | Edges | 24 |
  | Vertices | 14 |
  | Symmetry group | octahedral $(O_h)$ |
  
  The compound of cube and octahedron is a polyhedron which can be seen as either a polyhedral stellation or a compound.
  
  ## Construction
  
  The 14 Cartesian coordinates of the vertices of the compound are.
  
      6: (±2, 0, 0), ( 0, ±2, 0), ( 0, 0, ±2)
      8: ( ±1, ±1, ±1)
  
  ## As a compound
  
  It can be seen as the compound of an octahedron and a cube. It is one of four compounds constructed from a Platonic solid or Kepler-Poinsot polyhedron and its dual.
  
  It has octahedral symmetry $(O_h)$ and shares the same vertices as a rhombic dodecahedron.
  
  This can be seen as the three-dimensional equivalent of the compound of two squares ({8/2} "octagram"); this series continues on to infinity, with the four-dimensional equivalent being the compound of tesseract and 16-cell.
  
  | A cube and its dual octahedron | The intersection of both solids is the cuboctahedron, and their convex hull is the rhombic dodecahedron. |
  | - | - |
  
  ## As a stellation
  
  It is also the first stellation of the cuboctahedron and given as Wenninger model index 43.
  
  It can be seen as a cuboctahedron with square and triangular pyramids added to each face.
  
  The stellation facets for construction are:
  
  