Dodecagram

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

This is the only stellation of the dodecagon. The only other polygons with a single stellation are the pentagon, the octagon, and the decagon.

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


 * (±($\sqrt{6}$–1)/2, ±($\sqrt{2}$–1)/2),
 * (±1/2, ±(2–$\sqrt{6}$)/2).

Representations
A dodecagram has the following Coxeter diagrams:


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