Small icosacronic hexecontahedron

The small icosacronic hexecontahedron is a uniform dual polyhedron. It consists of 60 kites.

If its dual, the small icosicosidodecahedron, has an edge length of 1, then the short edges of the kites will measure $$\frac{\sqrt{30\left(65-19\sqrt5\right)}}{22} ≈ 1.18133$$, and the long edges will be $$\frac{\sqrt{30\left(85-\sqrt5\right)}}{38} ≈ 1.31129$$. ​The kite faces will have length $$3\frac{\sqrt{10\left(3517-585\sqrt5\right)}}{418} ≈ 1.06668$$, and width $$\sqrt5 ≈ 2.23607$$. ​The kites have two interior angles of $$\arccos\left(\frac34-\frac{\sqrt5}{20}\right) ≈ 50.34252°$$, one of $$\arccos\left(-\frac{1}{12}-\frac{19\sqrt5}{60}\right) ≈ 142.31856°$$, and one of $$\arccos\left(-\frac{5}{12}-\frac{\sqrt5}{60}\right) ≈ 116.99640°$$.

Vertex coordinates
A small icosacronic hexecontahedron with dual edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,0\right),$$
 * $$\left(±3\frac{5+7\sqrt5}{44},\,±3\frac{15-\sqrt5}{44},\,0\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(±3\frac{9\sqrt5-5}{76},\,±3\frac{15+11\sqrt5}{76},\,0\right),$$
 * $$\left(±3\frac{10+\sqrt5}{38},\,±3\frac{10+\sqrt5}{38},\,±3\frac{10+\sqrt5}{38}\right).$$