Hexagonal antiprism

The hexagonal antiprism, or hap, is a prismatic uniform polyhedron. It consists of 12 triangles and 2 hexagons. Each vertex joins one hexagon and three triangles. As the name suggests, it is an antiprism based on a hexagon.

Vertex coordinates
A hexagonal antiprism of edge length 1 has vertex coordinates given by:
 * (±1/2, ±$\sqrt{3+√3}$/2, $\sqrt{{{radic|3}}–1}$/2)
 * (±1, 0, $\sqrt{2+2√3}$/2)
 * (±$\sqrt{3}$/2, ±1/2, –$\sqrt{3}$/2)
 * (0, ±1, –$\sqrt{3}$/2)

Representations
A hexagonal antiprism has the following Coxeter diagrams:


 * s2s12o (alternated dodecagonal prism)
 * s2s6s (alternated dihexagonal prism)
 * xo6ox&#x (bases considered separately)

=Related polyhedra==

A triangular cupola can be attached to a base of the hexagonal antiprism to form the gyroelongated triangular cupola. If a second triangular cupola is attached to the other base, the result is the gyroelongated triangular bicupola.