![]() Cyclic: all corners lie on a single circle, called the circumcircle.Regular: both equilateral and equiangular.Equilateral: all edges are of the same length.Equiangular: all corner angles are equal.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°. Convex: any line drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice.Polygons may be characterized by their convexity or type of non-convexity: Polygons are primarily classified by the number of sides. Classification Some different types of polygon Number of sides It has been suggested that γόνυ ( gónu) 'knee' may be the origin of gon. The word polygon derives from the Greek adjective πολύς ( polús) 'much', 'many' and γωνία ( gōnía) 'corner' or 'angle'. There are many more generalizations of polygons defined for different purposes. Some sources also consider closed polygonal chains in Euclidean space to be a type of polygon (a skew polygon), even when the chain does not lie in a single plane.Ī polygon is a 2-dimensional example of the more general polytope in any number of dimensions. ![]() In contexts where one is concerned only with simple and solid polygons, a polygon may refer only to a simple polygon or to a solid polygon.Ī polygonal chain may cross over itself, creating star polygons and other self-intersecting polygons. The interior of a solid polygon is its body, also known as a polygonal region or polygonal area. A simple polygon is the boundary of a region of the plane that is called a solid polygon. More precisely, the only allowed intersections among the line segments that make up the polygon are the shared endpoints of consecutive segments in the polygonal chain. An n-gon is a polygon with n sides for example, a triangle is a 3-gon.Ī simple polygon is one which does not intersect itself. The points where two edges meet are the polygon's vertices or corners. The segments of a closed polygonal chain are called its edges or sides. In geometry, a polygon ( / ˈ p ɒ l ɪ ɡ ɒ n/) is a plane figure made up of line segments connected to form a closed polygonal chain. Some polygons of different kinds: open (excluding its boundary), boundary only (excluding interior), closed (including both boundary and interior), and self-intersecting. For other uses, see Polygon (disambiguation). ![]()
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