A simple polygon that is not convex is called concave, non-convex or reentrant. A simple concave polygon will always have an interior angle with a measure that is greater than 180 degrees.
It is always possible to partition 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).
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- Definition and properties of concave polygons with interactive animation.
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