title: Compound of two snub cubes
text: # Compound of two snub cubes
  
  Compound of two snub cubes :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{68}$ |
  | Schläfli symbol | βr{4,3} |
  | Coxeter diagram | |
  | Polyhedra | 2 snub cubes |
  | Faces | 16+48 triangles 12 squares |
  | Edges | 120 |
  | Vertices | 48 |
  | Symmetry group | octahedral $(O_h)$ |
  | Subgroup restricting to one constituent | chiral octahedral (O) |
  
  This uniform polyhedron compound is a composition of the 2 enantiomers of the snub cube. As a holosnub, it is represented by Schläfli symbol βr{4,3} and Coxeter diagram .
  
  The vertex arrangement of this compound is shared by a convex nonuniform truncated cuboctahedron, having rectangular faces, alongside irregular hexagons and octagons, each alternating with two edge lengths.
  
  Together with its convex hull, it represents the snub cube-first projection of the nonuniform snub cubic antiprism.
  
  ## Cartesian coordinates
  
  Cartesian coordinates for the vertices are all the permutations of
  
      (±1, ±ξ, ±1/ξ)
  
  where ξ is the real solution to
  
      $\xi ^{3}+\xi ^{2}+\xi =1,\,$
  
  which can be written
  
      $\xi ={\frac {1}{3}}\left({\sqrt[{3}]{17+3{\sqrt {33}}}}-{\sqrt[{3}]{-17+3{\sqrt {33}}}}-1\right)$
  
  or approximately 0.543689. ξ is the reciprocal of the tribonacci constant.
  
  Equally, the tribonacci constant, t, just like the snub cube, can compute the coordinates as:
  
      (±1, ±t, ±1/t)
  
  ## Truncated cuboctahedron
  
  This compound can be seen as the union of the two chiral alternations of a truncated cuboctahedron:
  
      A geometric construction of the Tribonacci constant (AC), with compass and marked ruler, according to the method described by Xerardo Neira.
  