Great ditrigonal dodecacronic hexecontahedron explained

In geometry, the great ditrigonal dodecacronic hexecontahedron (or great lanceal trisicosahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform great ditrigonal dodecicosidodecahedron. Its faces are kites. Part of each kite lies inside the solid, hence is invisible in solid models.

Proportions

Kite faces have two angles of

\arccos(	5	-
	12

	1
	4

\sqrt{5}) ≈ 98.18387249181^\circ

, one of

\arccos(-	5	+
	12

	1
	60

\sqrt{5}) ≈ 112.29645207354^\circ

and one of

\arccos(-	1	+
	12

	19
	60

\sqrt{5}) ≈ 51.33580294283^\circ

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

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

	31+5\sqrt{5

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