A complex polygon is a polygon which intersects itself. Therefore, unlike simple polygons, a complex polygon may not always be interpreted as a polygonal region.

A formula relating an integral over a region to a closed line integral may still apply when the "inside-out" part of the region is counted negatively.

Moving around the polygon, the total amount one "turns" at the vertices can be any integer times 360°, e.g. 720° for a pentagram and 0° for an angular "eight". See also orbit (dynamics).

A complex polygon which is equilateral and cyclic is called a star polygon.