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

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 ${\displaystyle \arccos({\frac {1}{4))+{\frac {1}{2)){\sqrt {2)))\approx 16.842\,116\,236\,30^{\circ ))$, 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 ${\displaystyle \arccos({\frac {-7-4{\sqrt {2))}{17)))\approx 138.117\,959\,055\,51^{\circ ))$. The ratio between the lengths of the long edges and the short ones equals ${\displaystyle 2-{\frac {1}{2)){\sqrt {2))\approx 1.292\,893\,218\,81}$.