A recursive construction for the dual polar spaces DQ(2n, 2)

New combinatorial constructions for the near hexagons I-3 and DQ(6, 2) in terms of ordered pairs of collinear points of the generalized quadrangle W(2) were given by Sahoo [B.K. Sahoo, New constructions of two slim dense near hexagons, Discrete Math. 308 (10) (2007) 2018-2024]. Replacing, W(2) by an arbitrary dual polar space of type DQ(2n, 2), n >= 2, 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 (s, t, T-2) = (2, 5, {1, 2}), J. Geom. 78 (2003) 50-58.] we show that these generalized constructions give rise to near 2n-gons which are isomorphic to I-n and DQ(2n, 2). In this way, we obtain a recursive construction for the dual polar spaces DQ(2n, 2), n >= 2, 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]