geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, the small hexacronic icositetrahedron is the dual of the

small cubicuboctahedron In geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13. It has 20 faces (8 triangles, 6 squares, and 6 octagons), 48 edges, and 24 vertices. Its vertex figure is a crossed quadrilateral. The small cubicuboctahedron ...

. It is visually identical to the

small rhombihexacron In geometry, the small rhombihexacron (or small dipteral disdodecahedron) is the dual of the small rhombihexahedron. It is visually identical to the small hexacronic icositetrahedron. Its faces are antiparallelograms formed by pairs of coplanar ...

. 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+\frac\sqrt)\approx 16.842\,116\,236\,30^

, one of

\arccos(\frac-\frac\sqrt)\approx 81.578\,941\,881\,85^

and one of

360^-\arccos(-\frac-\frac\sqrt)\approx 244.736\,825\,645\,55^

. Its

dihedral angles A dihedral angle is the angle between two intersecting planes or half-planes. In chemistry, it is the clockwise angle between half-planes through two sets of three atoms, having two atoms in common. In solid geometry, it is defined as the uni ...

equal

\arccos()\approx 138.117\,959\,055\,51^

. The ratio between the lengths of the long edges and the short ones equals

2-\frac\sqrt\approx 1.292\,893\,218\,81

References

External links

* Dual uniform polyhedra {{polyhedron-stub