Stellated hexadecagon

The stellated hexadecagon or shad is a polygon compound composed of two octagons. As such it has 16 edges and 16 vertices.

As the name suggests, it is the first stellation of the hexadecagon.

Its quotient prismatic equivalent is the octagonal antiprism, which is three-dimensional.

Vertex coordinates
Coordinates for a of edge length $\sqrt{2+√2}$, centered at the origin, are all permutations of:
 * $$\left(\pm1,\,0\right),$$
 * $$\left(\pm\frac{2+\sqrt2}{2},\,\pm\frac{2-\sqrt2}{2}\right),$$
 * $$\left(\pm\frac{\sqrt2}{2},\,\pm\frac{\sqrt2}{2}\right).$$