We characterize the point-distance-2-regular hexagons as the only hexagons for which the intersection sets have size one, and containing on ovoidal subspace all the points of which are 3-regular. We also give a characterization of the finite split Cayley hexagon of even order.
We characterize the dual of the generalized hexagons naturally associated to the groups G2(q) and 3D4(q) by looking at certain configurations, and also by considering intersections of traces. For instance, the dual of a generalized hexagon F of finite order (s, t) is associated to the Chevaliey groups mentioned above if and only if the intersection of any… (More)
We generalize the notion of a semi-aane plane to structures with higher girth n. We prove that, in the ÿnite case, for n odd, and with an additional assumption also for n even, these geometries, which we call forgetful n-gons, always arise from (ÿnite) generalized n-gons by 'forgetting' lines.