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

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 ${\displaystyle \arccos({\frac {1}{6)))\approx 80.405\,931\,773\,14^{\circ ))$, 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.