Medial deltoidal hexecontahedron

The medial deltoidal hexecontahedron is a uniform dual polyhedron. It consists of 60 kites.

If its dual, the rhombidodecadodecahedron, has an edge length of 1, then the short edges of the kites will measure $$3\frac{7\sqrt{30}-5\sqrt6}{110} ≈ 0.71163$$, and the long edges will be $$3\frac{5\sqrt6+7\sqrt{30}}{110} ≈ 1.37967$$. ​The kite faces will have length $$\frac{6\sqrt7}{11} ≈ 1.44314$$, and width $$\frac{3\sqrt5}{5} ≈ 1.34164$$. The kites have two interior angles of $$\arccos\left(\frac16\right) ≈ 80.40539°$$, one of $$\arccos\left(-\frac18+\frac{7\sqrt5}{24}\right) ≈ 58.18445°$$, and one of $$\arccos\left(-\frac18-\frac{7\sqrt5}{24}\right) ≈ 141.00369°$$.

Vertex coordinates
A medial deltoidal hexecontahedron with dual edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(±\frac{3\sqrt5}{5},\,0,\,0\right),$$
 * $$\left(±3\frac{7+\sqrt5}{22},\,±3\frac{3\sqrt5-1}{22},\,0\right),$$
 * $$\left(±3\frac{5-\sqrt5}{20},\,±\frac{3\sqrt5}{10},\,±3\frac{5+\sqrt5}{20}\right),$$
 * $$\left(±3\frac{1+3\sqrt5}{22},\,±3\frac{7-\sqrt5}{22},\,0\right).$$