Small ditrigonal dodecacronic hexecontahedron

Small ditrigonal dodecacronic hexecontahedron
Type	Star polyhedron
Face
Elements	F = 60, E = 120 V = 44 (χ = −16)
Symmetry group	Ih, [5,3], *532
Index references	DU43
dual polyhedron	Small ditrigonal dodecicosidodecahedron

File:Small ditrigonal dodecacronic hexecontahedron.stl 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 $\arccos (\frac{5}{12}+\frac{1}{4}\sqrt{5})\approx 12.66107880443^{\circ }$, one of $\arccos (-\frac{5}{12}-\frac{1}{60}\sqrt{5})\approx 116.99639685170^{\circ }$ and one of $360^{\circ }-\arccos (-\frac{1}{12}-\frac{19}{60}\sqrt{5})\approx 217.68144553945^{\circ }$. Its dihedral angles equal $\arccos (\frac{-44-3\sqrt{5}}{61})\approx 146.23065975553^{\circ }$. The ratio between the lengths of the long and short edges is $\frac{31+5\sqrt{5}}{38}\approx 1.11000894441$.