Great ditrigonal dodecacronic hexecontahedron

In geometry, the great ditrigonal dodecacronic hexecontahedron (or great lanceal trisicosahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform great ditrigonal dodecicosidodecahedron. Its faces are kites, having two angles of ${\displaystyle \arccos({\frac {5}{12}}-{\frac {1}{4}}{\sqrt {5}})\approx 98.183\,872\,491\,81^{\circ }}$, one of ${\displaystyle \arccos(-{\frac {5}{12}}+{\frac {1}{60}}{\sqrt {5}})\approx 112.296\,452\,073\,54^{\circ }}$ and one of ${\displaystyle \arccos(-{\frac {1}{12}}+{\frac {19}{60}}{\sqrt {5}})\approx 51.335\,802\,942\,83^{\circ }}$. Its dihedral angles equal ${\displaystyle \arccos({\frac {-44+3{\sqrt {5}}}{61}})\approx 127.686\,523\,427\,48^{\circ }}$. Part of each kite lies inside the solid, hence is invisible in solid models. The ratio between the lengths of the long edges and the short ones equals ${\displaystyle {\frac {31+5{\sqrt {5}}}{22}}\approx 1.917\,288\,176\,70}$.

Great ditrigonal dodecacronic hexecontahedron
Type	Star polyhedron
Face
Elements	F = 60, E = 120 V = 44 (χ = −16)
Symmetry group	Ih, [5,3], *532
Index references	DU42
dual polyhedron	Great ditrigonal dodecicosidodecahedron

3D model of a great ditrigonal dodecacronic hexecontahedron