Convex polygon
In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a simple polygon (not self-intersecting). Equivalently, a polygon is convex if every line that does not contain any edge intersects the polygon in at most two points. A strictly convex polygon is a convex polygonal such that no line contains two of its edges. In a convex polygon, all interior angles  are less than or equal to 180 degrees, while in a strictly convex polygon all interior angles are strictly less than 180 degrees. Properties. The following properties of a simple polygon are all equivalent to convexity: Additional properties of convex polygons include: Every polygon inscribed in a circle (such that all vertices of the polygon touch the circle), if not self-intersecting, is convex. However, not every convex polygon can be inscribed in a circle. Strict convexity. The following properties of a simple polygon are all equivalent to strict convexity: Every nondegenerate triangle is strictly convex.