New constructions of two slim dense near hexagons

Abstract

We provide a geometrical construction of the unique slim dense near hexagon with parameters (s,t,t2)=(2,5,{1,2}). Using this construction, we construct the rank 3 symplectic dual polar space DSp(6,2) which is the unique slim dense near hexagon with parameters (s,t,t2)=(2,6,2). Both near hexagons are constructed from two copies of the unique generalized quadrangle with parameters (2,2).