Star polygon
In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, certain notable ones can arise through truncation operations on regular simple and star polygons.
{5/2} |
|5/2| |
| A regular star pentagon, {5/2}, has five corner vertices and intersecting edges, while a concave decagon, |5/2|, has ten edges and two sets of five vertices. The first are used in definitions of star polyhedra and star uniform tilings, while the second are sometimes used in planar tilings. | |
Small stellated dodecahedron |
Tessellation |
Branko Grünbaum identified two primary definitions used by Johannes 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.
One definition of a star polygon, used in turtle graphics, is a polygon having 2 or more turns (turning number and density), like in spirolaterals.