title: Great triakis octahedron
text: # Great triakis octahedron
  
  Great triakis octahedron :
  
  | Type | Star polyhedron |
  | - | - |
  | Face | |
  | Elements | F = 24, E = 36 V = 14 (χ = 2) |
  | Symmetry group | $O_h,$ [4,3], *432 |
  | Index references | $DU_{19}$ |
  | dual polyhedron | Stellated truncated hexahedron |
  
  In geometry, the great triakis octahedron is the dual of the stellated truncated hexahedron $(U_{19}).$ It has 24 intersecting isosceles triangle faces. Part of each triangle lies within the solid, hence is invisible in solid models.
  
  ## Proportions
  
  The triangles have one angle of $\arccos({\frac {1}{4}}+{\frac {1}{2}}{\sqrt {2}})\approx 16.842\,116\,236\,30^{\circ }$ and two of $\arccos({\frac {1}{2}}-{\frac {1}{4}}{\sqrt {2}})\approx 81.578\,941\,881\,85^{\circ }$. The dihedral angle equals $\arccos({\frac {-3+8{\sqrt {2}}}{17}})\approx 60.722\,386\,809\,64^{\circ }$.
  
  