a polygon with all sides the same length is said to be equilateral.
a polygon with all sides the same length is said to be equilateral.
a polygon with all sides the same length is said to be?
equilateral
equilateral polygon









































in geometry, three or more than three straight lines (or segment of a line) make a polygon and an equilateral polygon is a polygon which has all sides of the same length. except in the triangle case, it need not be equiangular (need not have all angles equal), but if it does then it is a regular polygon. if the number of sides is at least five, an equilateral polygon need not be a convex polygon: it could be concave or even self-intersecting.









































section::::examples.









































all regular polygons and isotoxal polygons are equilateral.
equilateral polygon
the classification up to homeomorphism and diffeomorphism of compact riemann surfaces can be accomplished using the fundamental polygon. indeed as poincaré observed convex fundamental polygons for compact riemann surfaces "h"/γ can be constructed by adapting the method dirichlet from the euclidean space to hyperbolic space. then following nevanlinna and jost, the fundamental domain can be modified in steps to yield a non-convex polygon with vertices lying in a single orbit of γ and piecewise geodesic sides. the pairing relation on the sides is also modified in each of these steps. each step involves cutting the polygon by a diagonal geodesic segment in the interior of the polygon and reassembling the polygon using one of the möbius transformations involved in the pairing. no two paired sides can have a common vertex in the final pairing relation, which satisfies similar properties to the original relation. this polygon can in turn be successively modified by reassembling the polygon after cutting it by a diagonal piecewise geodesic segment in its interior. the final polygon has 4"g" equivalent vertices, with sides that are piecewise geodesic. the sides are labelled by the group elements which give the möbius transformation to the paired side. in order the labelling is
fundamental polygon