Regular Polygon
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For other uses, see Polygon (disambiguation).
Some polygons of different kinds
In geometry a polygon ( /ˈpɒlɪɡɒn/) is a flat shape consisting of straight lines that are joined to form a closed chain or circuit.
A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or corners. An ngon is a polygon with n sides. The interior of the polygon is sometimes called its body. A polygon is a 2dimensional example of the more general …show more content…
Miscellaneous
* Rectilinear: a polygon whose sides meet at right angles, i.e., all its interior angles are 90 or 270 degrees. * Monotone with respect to a given line L, if every line orthogonal to L intersects the polygon not more than twice.
Properties
Euclidean geometry is assumed throughout.
Angles
Any polygon, regular or irregular, selfintersecting or simple, has as many corners as it has sides. Each corner has several angles. The two most important ones are: * Interior angle – The sum of the interior angles of a simple ngon is (n − 2)π radians or (n − 2)180 degrees. This is because any simple ngon can be considered to be made up of (n − 2) triangles, each of which has an angle sum of π radians or 180 degrees. The measure of any interior angle of a convex regular ngon is radians or degrees. The interior angles of regular star polygons were first studied by Poinsot, in the same paper in which he describes the four regular star polyhedra. * Exterior angle – Tracing around a convex ngon, the angle "turned" at a corner is the exterior or external angle. Tracing all the way around the polygon makes one full turn, so the sum of the exterior angles must be

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