Stellated octagon

The stellated octagon, or soc is a polygon compound composed of two squares. As such it has 8 edges and 8 vertices.

It is the first stellation of the octagon.

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

Vertex coordinates
Coordinates for the vertices of a stellated octagon of edge length 1 centered at the origin are given by:
 * $$\left(±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2}\right).$$

Variations
The stellated octagon can be varied by changing the angle between the two component squares from the usual 45°. These 2-square compounds generally have a ditetragon as their convex hull and remain regular, but not uniform, with square symmetry only.