Small hexagrammic hexecontahedron

The small hexagrammic hexecontahedron is a uniform dual polyhedron. It consists of 60 mirror-symmetric unicursal hexagrams.

If its dual, the Small Inverted Retrosnub icosicosidodecahedron, has an edge length of 1, then the two short edges of each hexagram will measure $$\frac{\sqrt{13+7\sqrt5+\sqrt{22\left(9+5\sqrt5\right)}}}{6} ≈ 1.17524$$, and the four long edges will be $$\frac{\sqrt{9+3\sqrt5+\sqrt{2\left(51+23\sqrt5\right)}}}{2} ≈ 2.73958$$. The unicursal hexagrams have five interior angles of $$\arccos\left(\xi\right) ≈ 21.03199°$$, and one of $$360- \arccos\left(\phi^{-2}\xi-\phi^{-1}\right) ≈ 254.84055$$, where $$\xi = \frac{1}{4} + \frac{\sqrt{1+4\phi}}{4} ≈ 0.93338$$ , and $$\phi$$ is the golden ratio.

The dihedral angles are equal to $$\arccos(\xi/(1+\xi))\approx 61.133\,452\,273\,64^{\circ}$$