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	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 $\arccos({\frac {3}{4}}+{\frac {1}{20}}{\sqrt {5}})\approx 30.480\,324\,565\,36^{\circ }$ 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.