Stellated decagon

The stellated decagon or sadeg is a polygon compound composed of two pentagons. As such it has 10 edges and 10 vertices.

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

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

Vertex coordinates
Coordinates for the vertices of a stellated decagon of edge length 1 centered at the origin are given by:


 * $$\left(±\frac12,\,±\sqrt{\frac{5+2\sqrt5}{20}}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\sqrt{\frac{5-\sqrt5}{40}}\right),$$
 * $$\left(0,\,±\sqrt{\frac{5+\sqrt5}{10}}\right).$$

Variations
The stellated decagon can be varied by changing the angle between the two component pentagons from the usual 36°. These 2-pentagon compounds generally have a dipentagon as their convex hull and remain uniform,but not regular, with pentagonal symmetry only.