Great ditrigonal dodecacronic hexecontahedron

Great ditrigonal dodecacronic hexecontahedron

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

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.

Proportions

Kite faces have two angles of $\arccos({\frac {5}{12}}-{\frac {1}{4}}{\sqrt {5}})\approx 98.183\,872\,491\,81^{\circ }$ , one of $\arccos(-{\frac {5}{12}}+{\frac {1}{60}}{\sqrt {5}})\approx 112.296\,452\,073\,54^{\circ }$ and one of $\arccos(-{\frac {1}{12}}+{\frac {19}{60}}{\sqrt {5}})\approx 51.335\,802\,942\,83^{\circ }$ . Its dihedral angles equal $\arccos({\frac {-44+3{\sqrt {5}}}{61}})\approx 127.686\,523\,427\,48^{\circ }$ . The ratio between the lengths of the long edges and the short ones equals ${\frac {31+5{\sqrt {5}}}{22}}\approx 1.917\,288\,176\,70$ .

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.

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