Medial deltoidal hexecontahedron
# Medial deltoidal hexecontahedron

Medial deltoidal hexecontahedron :

| Type | Star polyhedron |
| - | - |
| Face | |
| Elements | F = 60, E = 120 V = 54 (χ = −6) |
| Symmetry group | $I_h,$ [5,3], *532 |
| Index references | $DU_{38}$ |
| dual polyhedron | Rhombidodecadodecahedron |

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.

## Proportions

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

