New constructions of two slim dense near hexagons

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We provide a geometrical construction of the 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 slim dense near hexagon with parameters (s,t,t₂)=(2,6,2). Both the near hexagons are constructed from two copies of a generalized quadrangle with parameters (2,2).