Pentagrammic antiprism

The pentagrammic antiprism, or stap, is a prismatic uniform polyhedron. It consists of 10 triangles and 2 pentagrams. Each vertex joins one pentagram and three triangles. As the name suggests, it is an antiprism based on a pentagram. It is one of two pentagrammic antiprisms, the other one being the pentagrammic retroprism. In this case, the pentagrams are aligned with one another.

Vertex coordinates
A pentagrammic antiprism of edge length 1 has vertex coordinates given by:
 * $$\left(±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,±\sqrt{\frac{\sqrt5-1}8}\right),$$
 * $$\left(±\frac{\sqrt5-1}4,\,\sqrt{\frac{5+\sqrt5}{40}},\,±\sqrt{\frac{\sqrt5-1}8}\right),$$
 * $$\left(0,\,-\sqrt{\frac{5-\sqrt5}{10}},\,±\sqrt{\frac{\sqrt5-1}8}\right).$$

Related polyhedra
Two non-prismatic uniform polyhedron compounds are composed of pentagrammic antiprisms:


 * Small snub dodecahedron (6)
 * Small disnub dodecahedron (12)

There are an infinite amount of prismatic uniform compounds that are the antiprisms of compounds of pentagrams.

In vertex figures
Pentagrammic antiprisms appear as vertex figures of four uniform polychora: the small prismatohecatonicosachoron, pentagrammal antiprismatoverted hexacosihecatonicosachoron, small pentagrammal antiprismatoverted dishecatonicosachoron, and great pentagrammal antiprismatoverted dishecatonicosachoron.