Convex polygon

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Convex polygon.png

A convex polygon is a polygon whose interior forms a convex set. That is, if any 2 points on the perimeter of the polygon are connected by a line segment, no point on that segment will be outside the polygon. For example, every regular polygon is convex.

All internal angles of a convex polygon are less than $180^{\circ}$. Equivalently, all external angles are less than $180^{\circ}$. The sum of the exterior angles of any convex polygon is $360^\circ$ and the sum of the internal angles of a convex $n$-gon is $(n - 2)180^\circ$.

The convex hull of a finite set of points is a convex polygon with some or all of the points as its vertices.

See also

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