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 , t 2 ) = ( 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 , t 2 ) = ( 2 , 6 , 2 ) . Both near hexagons are constructed from two copies of the unique generalized quadrangle with parameters (2,2).