Octagram

The octagram is a non-convex polygon with 8 sides. It's created by stellating the octagon. A regular octagram has equal sides and equal angles.

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

The octagram is the uniform quasitruncation of the square, and as such is the only regular star polygon to regularly appear in non-prismatic uniform polytopes in 5 dimensions and higher.

Vertex coordinates
Coordinates for an octagram of unit edge length, centered at the origin, are all permutations of
 * $$\left(±\frac{\sqrt2-1}{2},\,±\frac12\right).$$

Representations
An octagram has the following Coxeter diagrams:


 * x8/3o (full symmetry)
 * x4/3x (B2 symmetry)