We classify the generalized hexagons which are laxly embedded in projective space such that the embedding is flat and polarized. Besides the standard examples related to the hexagons defined over the algebraic groups of type $\ssG_2$, $^3\ssD_4$ and $^6\ssD_4$ (and occurring in projective dimensions $5,6,7$), we find new examples in unbounded dimension related to the mixed groups of type $\ssG_2$.

In this paper, we present a geometric construction of the Moufang quadrangles discovered by Richard Weiss (see Tits \& Weiss \cite{Tit-Wei:97} or Van Maldeghem \cite{Mal:97}). The construction uses fixed point free involutions in certain mixed quadrangles, which are then extended to involutions of certain buildings of type $\ssF_4$. The fixed flags of each such involution constitute a generalized quadrangle. This way, not only the new exceptional quadrangles can be constructed, but also some special type of mixed quadrangles.