Small icosacronic hexecontahedron explained

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

Proportions

The kites have two angles of

\arccos( (3)/(- 4) (1)/(20) \sqrt{ 5 }) ≈ 50 . 34252434387 ^{\circ} , one of \arccos( - (1)/(- 12) (19)/(60) \sqrt{ 5 }) ≈ 142 . 31855446055 ^{\circ} and one of \arccos( - (5)/(- 12) (1)/(60) \sqrt{ 5 }) ≈ 116 . 99639685170 ^{\circ} . The dihedral angle equals \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