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In geometry, a star polygon is a type of non-convex polygon. Only the regular star polygons have been studied in any depth; star polygons in general appear not to have been formally defined.

Two types of star pentagons
Alfkors.svg
{5/2}
Stjärna.svg
|5/2|
A regular star pentagon, {5/2}, has five corner vertices and intersecting edges, while concave decagon, |5/2|, has with ten edges and two sets of five vertices. The first are used in definitions of star polyhedra, while the second are used in planar tilings.
Small stellated dodecahedron.png
Small stellated dodecahedron
Kepler decagon pentagon pentagram tiling.png
Tessellation

In geometry, a star polygon is a type of non-convex polygon. Only the regular star polygons have been studied in any depth; star polygons in general appear not to have been formally defined.

Branko Grünbaum identified two primary definitions used by Kepler, one being the regular star polygons with intersecting edges that don't generate new vertices, and the second being simple isotoxal concave polygons.

The first usage is included in polygrams which includes polygons like the pentagram but also compound figures like the hexagram.