A characterization of the natural embedding of the split Cayley hexagon in by intersection numbers in finite projective spaces of arbitrary dimension.

Abstract: We prove that a non-empty set of at most lines of with the properties that (1) every point of is incident with either or elements of , (2) every plane of is incident with either , or elements of , (3) every solid of is incident with either , , or elements of , and (4) every four-dimensional subspace of is incident with at most elements of is necessarily the set of lines of a split Cayley hexagon naturally embedded in . [Copyright &y& Elsevier]