Great pentagrammic hexecontahedron

In geometry, the great pentagrammic hexecontahedron (or great dentoid ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the great retrosnub icosidodecahedron. Its 60 faces are irregular pentagrams.

Proportions
Denote the golden ratio by $$\phi$$. Let $$\xi\approx 0.946\,730\,033\,56$$ be the largest positive zero of the polynomial $$P = 8x^3-8x^2+\phi^{-2}$$. Then each pentagrammic 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 face has three long and two short edges. The ratio $$l$$ between the lengths of the long and the short edges is given by
 * $$l = \frac{2-4\xi^2}{1-2\xi}\approx 1.774\,215\,864\,94$$.

The dihedral angle equals $$\arccos(\xi/(\xi+1))\approx 60.901\,133\,713\,21^{\circ}$$. Part of each face lies inside the solid, hence is invisible in solid models. The other two zeroes of the polynomial $$P$$ play a similar role in the description of the great pentagonal hexecontahedron and the great inverted pentagonal hexecontahedron.