Octagrammic antiprism

The octagrammic antiprism, or stoap, is a prismatic uniform polyhedron. It consists of 16 triangles and 2 octagrams. Each vertex joins one octagram and three triangles. As the name suggests, it is an antiprism based on an octagram. It is one of two octagrammic antiprisms, the other one being the octagrammic retroprism.

Vertex coordinates
An octagrammic antiprism of edge length 1 has vertex coordinates given by:
 * $$\left(±\frac12,\,±\frac{\sqrt2-1}2,\,H\right),$$
 * $$\left(±\frac{\sqrt2-1}2,\,±\frac12,\,H\right),$$
 * $$\left(0,\,±\sqrt{\frac{2-\sqrt2}2},\,-H\right),$$
 * $$\left(±\sqrt{\frac{2-\sqrt2}2},\,0,\,-H\right),$$
 * $$\left(±\frac{\sqrt{2-\sqrt2}}2,\,±\frac{\sqrt{2-\sqrt2}}2,\,-H\right),$$

where $$H=\sqrt{\frac{-2+2\sqrt2+\sqrt{20-14\sqrt2}}8}$$ is the distance between the antiprism's center and the center of one of its bases.