  In the classification of Moufang polygons by J. Tits and R. Weiss, the most
intricate case is by far the case of the exceptional Moufang quadrangles of
type E_6, E_7 and E_8, and in fact, the construction that they present is
ad-hoc and lacking a deeper explanation. We will show how tensor products of
two composition algebras can be used to construct these Moufang quadrangles in
characteristic different from 2.
  As a byproduct, we will obtain a method to construct any Moufang quadrangle
in characteristic different from two from a module for a Jordan algebra.
