Robbins pentagon

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A Robbins pentagon is a cyclic polygon with 5 integer sides and integer area. It also has the property that all its diagonals are rational which means that it can be decomposed into Heron triangles. The converse is not necessarily true. Three Heron triangles cannot always be glued together in such a way that their exterior vertices lie on a circle. It is unknown whether or not an indecomposible Robbins pentagon exists.

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