Small ditrigonal dodecacronic hexecontahedron explained

In geometry, the small ditrigonal dodecacronic hexecontahedron (or fat star) is a nonconvex isohedral polyhedron. It is the dual of the uniform small ditrigonal dodecicosidodecahedron. It is visually identical to the small dodecicosacron. 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(	5	+
	12

	1
	4

\sqrt{5}) ≈ 12.66107880443^\circ

, one of

\arccos(-	5	-
	12

	1
	60

\sqrt{5}) ≈ 116.99639685170^\circ

and one of

360^\circ-\arccos(-

	1	-
	12

	19
	60

\sqrt{5}) ≈ 217.68144553945^\circ

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

}})\approx 146.230\,659\,755\,53^. The ratio between the lengths of the long and short edges is

	31+5\sqrt{5

}\approx 1.110\,008\,944\,41.