Great pentagrammic hexecontahedron

Great pentagrammic hexecontahedron is a uniform dual polyhedron. It consists of 60 mirror-symmetric pentagrams.

It is the dual of the great inverted retrosnub icosidodecahedron.

Each pentagram has three long and two short edges, the ratio between them is given by $$l = \frac{2-4\xi^2}{1-2\xi}\approx 1.774\,215\,864\,94$$.

Each face has four equal angles of $$\arccos(\xi)\approx 18.785\,633\,958\,24^{\circ}$$ and one angle of $$\arccos(-\phi^{-1}+\phi^{-2}\xi)\approx 104.857\,464\,167\,03^{\circ}$$.

Each dihedral angle is equal to $$\arccos(\xi/(\xi+1))\approx 60.901\,133\,713\,21^{\circ}$$,

where $$\xi\approx 0.946\,730\,033\,56$$ which is the largest positive root of the polynomial  and $$\phi$$ is the golden ratio