title: Great dodecicosacron
text: # Great dodecicosacron
  
  Great dodecicosacron :
  
  | Type | Star polyhedron |
  | - | - |
  | Face | |
  | Elements | F = 60, E = 120 V = 32 (χ = −28) |
  | Symmetry group | $I_h,$ [5,3], *532 |
  | Index references | $DU_{63}$ |
  | dual polyhedron | Great dodecicosahedron |
  
  In geometry, the great dodecicosacron (or great dipteral trisicosahedron) is the dual of the great dodecicosahedron $(U_{63}).$ It has 60 intersecting bow-tie-shaped faces.
  
  ## Proportions
  
  Each face has two angles of $\arccos({\frac {3}{4}}+{\frac {1}{20}}{\sqrt {5}})\approx 30.480\,324\,565\,36^{\circ }$ and two angles of $\arccos(-{\frac {5}{12}}+{\frac {1}{4}}{\sqrt {5}})\approx 81.816\,127\,508\,183^{\circ }$. The diagonals of each antiparallelogram intersect at an angle of $\arccos({\frac {5}{12}}-{\frac {1}{60}}{\sqrt {5}})\approx 67.703\,547\,926\,46^{\circ }$. The dihedral angle equals $\arccos({\frac {-44+3{\sqrt {5}}}{61}})\approx 127.686\,523\,427\,48^{\circ }$. The ratio between the lengths of the long edges and the short ones equals ${\frac {1}{2}}+{\frac {1}{2}}{\sqrt {5}}$, which is the golden ratio. Part of each face lies inside the solid, hence is invisible in solid models.
  
  