Great icosacronic hexecontahedron

In geometry, the great icosacronic hexecontahedron (or great sagittal trisicosahedron) is the dual of the great icosicosidodecahedron. Its faces are darts. A part of each dart lies inside the solid, hence is invisible in solid models.

Proportions
Faces have two angles of $$\arccos(\frac{3}{4}+\frac{1}{20}\sqrt{5})\approx 30.480\,324\,565\,36^{\circ}$$, one of $$\arccos(-\frac{1}{12}+\frac{19}{60}\sqrt{5})\approx 51.335\,802\,942\,83^{\circ}$$ and one of $$360^{\circ}-\arccos(-\frac{5}{12}+\frac{1}{60}\sqrt{5})\approx 247.703\,547\,926\,46^{\circ}$$. Its dihedral angles equal $$\arccos({\frac{-44+3\sqrt{5}}{61}})\approx 127.686\,523\,427\,48^{\circ}$$. The ratio between the lengths of the long and short edges is $$\frac{31+5\sqrt{5}}{22}\approx 1.917\,288\,176\,70$$.