Decagram

The decagram is a star polygon with 10 sides. A regular decagram has equal sides and equal angles.

It is the second stellation of the decagon, and the only one that is not a compound. The only other polygons with a single non-compound stellation are the pentagon, the octagon, and the dodecagon.

It is the uniform quasitruncation of the pentagram, and as such appears frequently in uniform polyhedra and polychora. It is the largest uniform star polygon to appear in a non-prismatic uniform polytope in 3 or 4 dimensions.

Vertex coordinates
Coordinates for a decagram of unit edge length, centered at the origin, are:


 * $$\left(±\frac12,\,±\frac{\sqrt{5-2\sqrt5}}2\right),$$
 * $$\left(±\frac{3-\sqrt5}4,\,±\sqrt{\frac{5-\sqrt5}8}\right),$$
 * $$\left(±\frac{\sqrt5-1}2,\,0\right).$$

Representations
A decagram has the following Coxeter diagrams:


 * x10/3o (full symmetry)
 * x5/3x (H2 symmetry)