a polygon such that there is a straight line that cuts it in four or more points

a polygon that is not convex

a polygon in which at least one segment connecting two vertices is outside the polygon

A polygon with at least one interior angle with measure greater than 180 degrees.

A polygon with one or more diagonals that have points outside the polygon.

A polygon with notches or concave areas along its perimeter (as opposed to convex polygon). A five-pointed star is an example of a concave polygon. To determine if a polygon is concave, apply the rubber band test. If an imaginary rubber band placed around the outside of a polygon would not touch all sides, then the polygon is concave. Concave polygons must be triangulated (formed into various triangles) before they can be rendered.