Medial deltoidal hexecontahedron

In geometry, the medial deltoidal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the rhombidodecadodecahedron. Its 60 intersecting quadrilateral faces are kites.

Medial deltoidal hexecontahedron
Type	Star polyhedron
Face
Elements	F = 60, E = 120 V = 54 (χ = −6)
Symmetry group	Ih, [5,3], *532
Index references	DU38
dual polyhedron	Rhombidodecadodecahedron

3D model of a medial deltoidal hexecontahedron

Proportions

The kites have two angles of ${\displaystyle \arccos({\frac {1}{6}})\approx 80.405\,931\,773\,14^{\circ }}$, one of ${\displaystyle \arccos(-{\frac {1}{8}}+{\frac {7}{24}}{\sqrt {5}})\approx 58.184\,446\,117\,59^{\circ }}$ and one of ${\displaystyle \arccos(-{\frac {1}{8}}-{\frac {7}{24}}{\sqrt {5}})\approx 141.003\,690\,336\,13^{\circ }}$. The dihedral angle equals ${\displaystyle \arccos(-{\frac {5}{7}})\approx 135.584\,691\,402\,81^{\circ }}$. The ratio between the lengths of the long and short edges is ${\displaystyle {\frac {27+7{\sqrt {5}}}{22}}\approx 1.938\,748\,901\,931\,75}$. Part of each kite lies inside the solid, hence is invisible in solid models.

References

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

External links

• Weisstein, Eric W. "Medial deltoidal hexecontahedron". MathWorld.
• Uniform polyhedra and duals