Small hexacronic icositetrahedron

In geometry, the small hexacronic icositetrahedron is the dual of the small cubicuboctahedron. It is visually identical to the small rhombihexacron. A part of each dart lies inside the solid, hence is invisible in solid models.

Proportions
Its faces are darts, having two angles of $$\arccos(\frac{1}{4}+\frac{1}{2}\sqrt{2})\approx 16.842\,116\,236\,30^{\circ}$$, one of $$\arccos(\frac{1}{2}-\frac{1}{4}\sqrt{2})\approx 81.578\,941\,881\,85^{\circ}$$ and one of $$360^{\circ}-\arccos(-\frac{1}{4}-\frac{1}{8}\sqrt{2})\approx 244.736\,825\,645\,55^{\circ}$$. Its dihedral angles equal $$\arccos({\frac{-7-4\sqrt{2}}{17}})\approx 138.117\,959\,055\,51^{\circ}$$. The ratio between the lengths of the long edges and the short ones equals $$2-\frac{1}{2}\sqrt{2}\approx 1.292\,893\,218\,81$$.