Stellated decagram

The stellated decagram or sadag is a polygon compound composed of two pentagrams. As such it has 10 edges and 10 vertices.

It is the third stellation of the decagon.

Its quotient prismatic equivalent is the pentagrammic retroprism, which is three-dimensional.

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


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

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