Maldeghem, Embedded thick finite generalized hexagons in projective space

We show that every embedded finite thick generalized hexagon J£ " of order (s, t) in PG(n, q) which satisfies the conditions (0 s = q, (ii) the set of all points of Jf generates PG(n, q), (iii) for any point x of Jf, the set of all points collinear in Jtf with x is contained in a plane of PG(n,q), (iv) for any point x of Jif, the set of all points of Jf not opposite x in Jf is contained in a hyperplane ofPG(n,q), is necessarily the standard representation of H(q) in PG(6,q) (on the quadric Q(6,q)), the standard representation of H(q) for q even in PG(5, q) (inside a symplectic space), or the standard representation of H(q, ^/q) in PG(7, q) (where the lines of jf are the lines fixed by a triality on the quadric Q + (7, q)). This generalizes a result by Cameron and Kantor [3], which is used in our proof. 1