  It is shown that the structure of the generalized quadrangle of order two is
fully encoded in the properties of the Desargues configuration. A point of the
quadrangle is represented by a geometric hyperplane of the Desargues
configuration and its line by a set of three hyperplanes such that one of them
is the complement of the symmetric difference of the remaining two and they all
share a pair of non-collinear points.
