Heptagonal antiprism

The heptagonal antiprism, or heap, is a prismatic uniform polyhedron. It consists of 14 triangles and 2 heptagons. Each vertex joins one heptagon and three triangles. As the name suggests, it is an antiprism based on a heptagon.

Vertex coordinates
The vertices of a heptagonal antiprism, centered at the origin and with edge length 2sin(π/7), are given by the following points, as well as their central inversions: where $$H=\sqrt{\frac{1+2\cos\frac\pi7}{8+8\cos\frac\pi7}}.$$
 * $$\left(1,\,0,\,H\right),$$
 * $$\left(\cos\left(\frac{2\pi}7\right),\,±\sin\left(\frac{2\pi}7\right),\,H\right),$$
 * $$\left(\cos\left(\frac{4\pi}7\right),\,±\sin\left(\frac{4\pi}7\right),\,H\right),$$
 * $$\left(\cos\left(\frac{6\pi}7\right),\,±\sin\left(\frac{6\pi}7\right),\,H\right),$$