Great icosacronic hexecontahedron
Type	Star polyhedron
Face
Elements	F = 60, E = 120 V = 52 (χ = −8)
Symmetry group	Ih, [5,3], *532
Index references	DU48
dual polyhedron	Great icosicosidodecahedron

In geometry, the great icosacronic hexecontahedron (or great sagittal trisicosahedron) is the dual of the great icosicosidodecahedron. Its faces are darts. A part of each dart lies inside the solid, hence is invisible in solid models.

Proportions

Faces have two angles of ${\displaystyle \arccos({\frac {3}{4))+{\frac {1}{20)){\sqrt {5)))\approx 30.480\,324\,565\,36^{\circ ))$, one of ${\displaystyle \arccos(-{\frac {1}{12))+{\frac {19}{60)){\sqrt {5)))\approx 51.335\,802\,942\,83^{\circ ))$ and one of ${\displaystyle 360^{\circ }-\arccos(-{\frac {5}{12))+{\frac {1}{60)){\sqrt {5)))\approx 247.703\,547\,926\,46^{\circ ))$. Its dihedral angles equal ${\displaystyle \arccos({\frac {-44+3{\sqrt {5))}{61)))\approx 127.686\,523\,427\,48^{\circ ))$. The ratio between the lengths of the long and short edges is ${\displaystyle {\frac {31+5{\sqrt {5))}{22))\approx 1.917\,288\,176\,70}$.