Great dodecacronic hexecontahedron

The great dodecacronic hexecontahedron is a uniform dual polyhedron. It consists of 60 kites.

If its dual, the great dodecicosidodecahedron, has an edge length of 1, then the short edges of the kites will measure $$2\frac{\sqrt{2\left(5-2\sqrt5\right)}}{3} ≈ 0.68499$$, and the long edges will be $$2\frac{\sqrt{65-19\sqrt5}}{11} ≈ 0.86272$$. ​The kite faces will have length $$\frac{\sqrt{10\left(157-31\sqrt5\right)}}{33} ≈ 0.89731$$, and width $$\sqrt5-1 ≈ 1.23607$$. ​The kites have two interior angles of $$\arccos\left(\frac58-\frac{\sqrt5}{8}\right) ≈ 69.78820°$$, one of $$\arccos\left(-\frac14+\frac{\sqrt5}{10}\right) ≈ 91.51239°$$, and one of $$\arccos\left(-\frac18-\frac{9\sqrt5}{40}\right) ≈ 128.91121°$$.

Vertex coordinates
A great dodecacronic hexecontahedron with dual edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{3-\sqrt5}{2},\,0\right),$$
 * $$\left(±\frac{25-9\sqrt5}{22},\,±\frac{15-\sqrt5}{22},\,0\right),$$
 * $$\left(±\frac{5-\sqrt5}{6},\,±\frac{3\sqrt5-5}{6},\,0\right),$$
 * $$\left(±\frac{4\sqrt5-5}{11},\,±\frac{4\sqrt5-5}{11},\,±\frac{4\sqrt5-5}{11}\right).$$