structural:expansion, quality:correction
Non-convex

There exist infinitely many non-convex regular polytopes in two dimensions, whose Schläfli symbols consist of rational numbers {n/m}. They are called star polygons and share the same vertex arrangements of the convex regular polygons.

In general, for any natural number n, there are n-pointed non-convex regular polygonal stars with Schläfli symbols { n / m } for all m such that m < n /2 (strictly speaking { n / m } = { n /(n − m)}) and m and n are coprime.