A Robbins pentagon, named after David P. Robbins

David P. Robbins

David P. Robbins was an American mathematician. He is most famous for introducing alternating sign matrices and his work on generalized Heron's formula....

, is a cyclic polygon with five integer sides and integer area. It also has the property that all its diagonal

Diagonal

A diagonal is a line joining two nonconsecutive vertices of a polygon or polyhedron. Informally, any sloping line is called diagonal. The word "diagonal" derives from the Greek διαγώνιος , from dia- and gonia ; it was used by both Strabo and Euclid to refer to a line connecting two vertices of a...

s are rational

Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number...

, 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.