Small hexagonal hexecontahedron

The small hexagonal hexecontahedron is a uniform dual polyhedron. It consists of 60 mirror-symmetric hexagons.

If its dual, the small snub icosicosidodecahedron, has an edge length of 1, then the two short edges of each hexagon will measure $$\frac{\sqrt{13+7\sqrt5-\sqrt{22\left(9+5\sqrt5\right)}}}{6} ≈ 0.45892$$, and the four long edges will be $$\frac{\sqrt{9+3\sqrt5-\sqrt{2\left(51+23\sqrt5\right)}}}{2} ≈ 0.59061$$. The hexagons have five interior angles of $$\arccos\left(\xi\right) ≈ 115.68227°$$, and one of $$\arccos\left(\phi^{-2}\xi-\phi^{-1}\right) ≈ 141.58866°$$, where $$\xi = \frac{1-\sqrt{1+4\phi}}{4} ≈ -0.43338$$, and $$\phi$$ is the golden ratio.

Vertex coordinates
A small hexagonal hexecontahedron with dual edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(±\frac{\sqrt{3+2\sqrt5}}{2},\,±\frac{\sqrt5-1}{4},\,0\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,0\right),$$
 * $$\left(±\frac{\sqrt5-1+\sqrt{2\left(3\sqrt5-1\right)}}{8},\,±\frac{\sqrt{3+2\sqrt5}-1}{4},\,±\frac{3-\sqrt5+\sqrt{2\left(19+9\sqrt5\right)}}{8}\right),$$
 * $$\left(±\frac{3+\sqrt5+\sqrt{2\left(19+9\sqrt5\right)}}{12},\,±\frac{\sqrt{1+\sqrt5+2\sqrt{\left(3+2\sqrt5\right)}}}{12},\,0\right),$$
 * $$\left(±\frac{1-\sqrt5+\sqrt{2\left(3\sqrt5-1\right)}}{8},\,\frac{1+\sqrt{3+2\sqrt5}}{4},\,±\frac{\sqrt5-3+\sqrt{2\left(19+9\sqrt5\right)}}{8}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right).$$