title: Cubitruncated cuboctahedron
text: In geometry, the cubitruncated cuboctahedron or cuboctatruncated cuboctahedron is a nonconvex uniform polyhedron, indexed as U16. It has 20 faces (8 hexagons, 6 octagons, and 6 octagrams), 72 edges, and 48 vertices, and has a shäfli symbol of tr{4,3/2}
  
  Convex hull 
  
  Its convex hull is a nonuniform truncated cuboctahedron.
  
  Orthogonal projection
  
  Cartesian coordinates 
  Cartesian coordinates for the vertices of a cubitruncated cuboctahedron are all the permutations of
  
   (±(−1), ±1, ±(+1))
  
  Related polyhedra
  
  Tetradyakis hexahedron
  
  The tetradyakis hexahedron (or great disdyakis dodecahedron) is a nonconvex isohedral polyhedron. It has 48 intersecting scalene triangle faces, 72 edges, and 20 vertices.
  
  Proportions 
  The triangles have one angle of , one of  and one of . The dihedral angle equals . Part of each triangle lies within the solid, hence is invisible in solid models.
  
  It is the dual of the uniform cubitruncated cuboctahedron.
  
  See also 
   List of uniform polyhedra
  
  References
  
   p. 92
  
  External links 
   
   
   http://gratrix.net Uniform polyhedra and duals
  
  Uniform polyhedra