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.

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.