title: Compound of ten truncated tetrahedra
text: # Compound of ten truncated tetrahedra
  
  Compound of ten truncated tetrahedra :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{56}$ |
  | Polyhedra | 10 truncated tetrahedra |
  | Faces | 40 triangles, 40 hexagons |
  | Edges | 180 |
  | Vertices | 120 |
  | Symmetry group | icosahedral $(I_h)$ |
  | Subgroup restricting to one constituent | chiral tetrahedral (T) |
  
  This uniform polyhedron compound is a composition of 10 truncated tetrahedra, formed by truncating each of the tetrahedra in the compound of 10 tetrahedra. It also results from composing the two enantiomers of the compound of 5 truncated tetrahedra.
  
  ## Cartesian coordinates
  
  Cartesian coordinates for the vertices of this compound are all the even permutations of
  
      (±1, ±1, ±3)
      $(±τ^{−1},$ $±(−τ^{−2}),$ ±2τ)
      (±τ, $±(−2τ^{−1}),$ $±τ^2)$
      $(±τ^2,$ $±(−τ^{−2}),$ ±2)
      (±(2τ−1), ±1, ±(2τ − 1))
  
  where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
  
  