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. Part of each kite lies inside the solid, hence is invisible in solid models.

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

Proportions

Kite faces have 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 ${\displaystyle \arccos({\frac {-44+3{\sqrt {5}}}{61}})\approx 127.686\,523\,427\,48^{\circ }}$. The ratio between the lengths of the long edges and the short ones equals ${\displaystyle {\frac {31+5{\sqrt {5}}}{22}}\approx 1.917\,288\,176\,70}$.

References

• Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208 p. 62

External links

• Weisstein, Eric W. "Great ditrigonal dodecacronic hexecontahedron". MathWorld.