title: Compound of six tetrahedra
text: # Compound of six tetrahedra
  
  Compound of six tetrahedra :
  
  | Type | Uniform compound |
  | - | - |
  | Convex hull | Nonuniform truncated octahedron |
  | Index | $UC_3$ |
  | Polyhedra | 6 tetrahedra |
  | Faces | 24 triangles |
  | Edges | 36 |
  | Vertices | 24 |
  | Symmetry group | octahedral $(O_h)$ |
  | Subgroup restricting to one constituent | 2-fold antiprismatic $(D_{2d})$ |
  
  The compound of six tetrahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 6 tetrahedra. It can be constructed by inscribing a stella octangula within each cube in the compound of three cubes, or by stellating each octahedron in the compound of three octahedra.
  
  It is one of only five polyhedral compounds (along with the compound of two great dodecahedra, the compound of five great dodecahedra, the compound of two small stellated dodecahedra, and the compound of five small stellated dodecahedra) which is vertex-transitive and face-transitive but not edge-transitive.
  
  