A recursive construction for the dual polar spaces image Original Research Article

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].