In geometry, a convex polygon is a simple polygon whose interior is a convex set. The following properties of a simple polygon are all equivalent to convexity:

• Every internal angle is at most 180 degrees.
• Every line segment between two vertices of the polygon does not go exterior to the polygon (i.e., it remains inside or on the boundary of the polygon).

A simple polygon is strictly convex if every internal angle is strictly less than 180 degrees. Equivalently, a polygon is strictly convex if every line segment between two vertices of the polygon is strictly interior to the polygon except at its endpoints.

Every triangle is strictly convex.

Concave polygon

If a simple polygon is not convex, it is called concave. At least one internal angle of a concave polygon is larger than 180 degrees.

A concave polygon is often called re-entrant polygon (but in some cases the latter term has a different meaning).

See also

• Happy Ending problem

Convex geometry | Polygons