Great triakis icosahedron

In geometry, the great triakis icosahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform great stellated truncated dodecahedron. Its faces are isosceles triangles. Part of each triangle lies within the solid, hence is invisible in solid models.

Proportions
The triangles have one angle of $$\arccos(-\frac{3}{20}+\frac{3}{20}\sqrt{5})\approx 79.314\,951\,312\,25^{\circ}$$ and two of $$\arccos(\frac{3}{4}-\frac{1}{20}\sqrt{5})\approx 50.342\,524\,343\,87^{\circ}$$. The dihedral angle equals $$\arccos(\frac{-24+15\sqrt{5}}{61})\approx 81.001\,410\,024\,84^{\circ}$$.