Abstract :
New combinatorial constructions for the near hexagons image and image in terms of ordered pairs of collinear points of the generalized quadrangle image were given by Sahoo [B.K. Sahoo, New constructions of two slim dense near hexagons. Discrete Math. (in press)]. Replacing image by an arbitrary dual polar space of type image, image, we obtain a generalization of these constructions. By using a construction alluded to in [B. De Bruyn, A new geometrical construction for the near hexagon with parameters image, J. Geom. 78 (2003) 50–58.] we show that these generalized constructions give rise to near image-gons which are isomorphic to image and image. In this way, we obtain a recursive construction for the dual polar spaces image, image, different from the one given in [B.N. Cooperstein, E.E. Shult, Combinatorial construction of some near polygons, J. Combin. Theory Ser. A 78 (1997) 120–140].
