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High Quality Content by WIKIPEDIA articles! In geometry, a polygon can be either convex or concave. A polygon that is not convex is called concave or reentrant. A concave polygon will always have an interior angle with a measure that is greater than 180 degrees. It is possible to cut a concave polygon into a set of convex polygons. A polynomial-time algorithm for finding a decomposition into as few convex polygons as possible is described by Chazelle & Dobkin (1985).