A Robbins pentagon, named after David P. Robbins, is a cyclic polygon with five integer sides and integer area. It also has the property that all its diagonals are rational, meaning 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 indecomposable Robbins pentagon exists.
D. P. Robbins, "Areas of Polygons Inscribed in a Circle", Discrete and Computational Geometry, volume 12, number 1, pages 223–236, 1994.