Great icosacronic hexecontahedron

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.

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

3D model of a great icosacronic hexecontahedron

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 ${\displaystyle {\frac {31+5{\sqrt {5}}}{22}}\approx 1.917\,288\,176\,70}$.

References

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

External links

Weisstein, Eric W. "Great icosacronic hexecontahedron". MathWorld.