title: Compound of two truncated tetrahedra
text: # Compound of two truncated tetrahedra
  
  Compound of two truncated tetrahedra :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{54}$ |
  | Schläfli symbol | $a_2{4,3}$ |
  | Coxeter diagram | + = |
  | Polyhedra | 2 truncated tetrahedra |
  | Faces | 8 triangles 8 hexagons |
  | Edges | 36 |
  | Vertices | 24 |
  | Symmetry group | octahedral $(O_h)$ [4,3] |
  | Subgroup restricting to one constituent | tetrahedral $(T_d)$ [3,3] |
  
  This uniform polyhedron compound is a composition of two truncated tetrahedra, formed by truncating each of the tetrahedra in the stellated octahedron. It is related to the cantic cube construction of the truncated tetrahedron, as , which is one of the two dual positions represented in this compound.
  
  The vertex arrangement is the same as a convex, but nonuniform rhombicuboctahedron having 12 rectangular faces.
  
  