Great dodecicosacron
Type	Star polyhedron
Face
Elements	F = 60, E = 120 V = 32 (χ = −28)
Symmetry group	Ih, [5,3], *532
Index references	DU63
dual polyhedron	Great dodecicosahedron

In geometry, the great dodecicosacron (or great dipteral trisicosahedron) is the dual of the great dodecicosahedron (U₆₃). It has 60 intersecting bow-tie-shaped faces.

Proportions

Each face has two angles of ${\displaystyle \arccos({\frac {3}{4))+{\frac {1}{20)){\sqrt {5)))\approx 30.480\,324\,565\,36^{\circ ))$ and two angles of ${\displaystyle \arccos(-{\frac {5}{12))+{\frac {1}{4)){\sqrt {5)))\approx 81.816\,127\,508\,183^{\circ ))$. The diagonals of each antiparallelogram intersect at an angle of ${\displaystyle \arccos({\frac {5}{12))-{\frac {1}{60)){\sqrt {5)))\approx 67.703\,547\,926\,46^{\circ ))$. The dihedral angle equals ${\displaystyle \arccos({\frac {-44+3{\sqrt {5))}{61)))\approx 127.686\,523\,427\,48^{\circ ))$. The ratio between the lengths of the long edges and the short ones equals ${\displaystyle {\frac {1}{2))+{\frac {1}{2)){\sqrt {5))}$, which is the golden ratio. Part of each face lies inside the solid, hence is invisible in solid models.