![]() A polygon cannot be both a star and star-shaped. Star polygon: a polygon which self-intersects in a regular way.The term complex is sometimes used in contrast to simple, but this usage risks confusion with the idea of a complex polygon as one which exists in the complex Hilbert plane consisting of two complex dimensions. Self-intersecting: the boundary of the polygon crosses itself. ![]() The polygon must be simple, and may be convex or concave. Star-shaped: the whole interior is visible from at least one point, without crossing any edge.There is at least one interior angle greater than 180°. Simple: the boundary of the polygon does not cross itself.Equivalently, there exists a line segment between two boundary points that passes outside the polygon. Non-convex: a line may be found which meets its boundary more than twice.This condition is true for polygons in any geometry, not just Euclidean. Equivalently, any line segment with endpoints on the boundary passes through only interior points between its endpoints. As a consequence, all its interior angles are less than 180°. ![]()
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