Great stellapentakis dodecahedron

In geometry, the great stellapentakis dodecahedron (or great astropentakis dodecahedron) is a nonconvex isohedral polyhedron. It is the dual of the truncated great icosahedron. It has 60 intersecting triangular faces.

Proportions
The triangles have one angle of $$\arccos(-\frac{7}{36}-\frac{1}{4}\sqrt{5})\approx 138.891\,114\,686\,59^{\circ}$$ and two of $$\arccos(\frac{3}{4}+\frac{1}{12}\sqrt{5})\approx 20.554\,442\,656\,71^{\circ}$$. The dihedral angle equals $$\arccos(\frac{-80+9\sqrt{5}}{109})\approx 123.320\,065\,258\,47^{\circ}$$. Part of each triangle lies within the solid, hence is invisible in solid models.