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