Convex polygon

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A convex pentagon
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A convex pentagon

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:

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.

[edit] Concave polygon

A simple concave hexagon
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A simple concave hexagon

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).

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