  We give a uniform construction of the finite simple groups $E_6(q)$, $F_4(q)$
and ${}^2E_6(q)$, which does not require any special treatment for
characteristics 2 or 3, and in particular avoids any mention of quadratic
Jordan algebras. Although almost all the ingredients can already be found
scattered through research papers spanning more than a century, a coherent,
sef-contained, account is hard to find in the literature.
