Equilateral pentagon

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In geometry, an equilateral pentagon is a polygon in the Euclidean plane with five sides of equal length. Its five vertex angles can take a range of sets of values, thus permitting it to form a family of pentagons. In contrast, the regular pentagon is unique, because it is equilateral and moreover it is equiangular (its five angles are equal; the measure is 108 degrees).

Four intersecting equal circles arranged in a closed chain are sufficient to determine a convex equilateral pentagon. Each circle's center is one of four vertices of the pentagon. The remaining vertex is determined by one of the intersection points of the first and the last circle of the chain.