Small hexacronic icositetrahedron

In geometry, the small hexacronic icositetrahedron is the dual of the small cubicuboctahedron. It is visually identical to the small rhombihexacron. Its faces are darts, having two angles of ${\displaystyle \arccos({\frac {1}{4}}+{\frac {1}{2}}{\sqrt {2}})\approx 16.842\,116\,236\,30^{\circ }}$, one of ${\displaystyle \arccos({\frac {1}{2}}-{\frac {1}{4}}{\sqrt {2}})\approx 81.578\,941\,881\,85^{\circ }}$ and one of ${\displaystyle 360^{\circ }-\arccos(-{\frac {1}{4}}-{\frac {1}{8}}{\sqrt {2}})\approx 244.736\,825\,645\,55^{\circ }}$. Its dihedral angles equal ${\displaystyle \arccos({\frac {-7-4{\sqrt {2}}}{17}})\approx 138.117\,959\,055\,51^{\circ }}$. A part of each dart lies inside the solid, hence is invisible in solid models.

Small hexacronic icositetrahedron
Type	Star polyhedron
Face
Elements	F = 24, E = 48 V = 20 (χ = −4)
Symmetry group	Oh, [4,3], *432
Index references	DU13
dual polyhedron	Small cubicuboctahedron

3D model of a small hexacronic icositetrahedron