Great icosacronic hexecontahedron explained

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(	3	+
	4

	1
	20

\sqrt{5}) ≈ 30.48032456536^\circ

, one of

\arccos(-	1	+
	12

	19
	60

\sqrt{5}) ≈ 51.33580294283^\circ

and one of

360^\circ-\arccos(-

	5	+
	12

	1
	60

\sqrt{5}) ≈ 247.70354792646^\circ

. Its dihedral angles equal

\arccos({	-44+3\sqrt{5

}})\approx 127.686\,523\,427\,48^. The ratio between the lengths of the long and short edges is

	31+5\sqrt{5

}\approx 1.917\,288\,176\,70.