Dodecagram

The dodecagram, or dodag, is a star polygon with 12 sides. A regular dodecagram has equal sides and equal angles.

This is the fourth stellation of the dodecagon, 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 decagon.

It is the uniform quasitruncation of the hexagon, and as such appears as faces in a handful of uniform Euclidean tilings. It is the largest star polygon known to appear in any non-prismatic spherical or Euclidean uniform polytopes.

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


 * $$\left(±\frac{\sqrt3-1}2,\,±\frac{\sqrt3-1}2\right),$$
 * $$\left(±\frac12,\,±\frac{2-\sqrt3}2\right).$$

Representations
A dodecagram has the following Coxeter diagrams:


 * x12/5o (full symmetry)
 * x6/5x (G2 symmetry)