  The classical Tits construction provides models of the exceptional simple Lie
algebras in terms of a unital composition algebra and a degree three simple
Jordan algebra. A couple of actions of the symmetric group of degree 4 on this
construction are given. By means of these actions, the models provided by the
Tits construction are related to models of the exceptional Lie algebras
obtained from two different types of structurable algebras. Some models of
exceptional Lie superalgebras are discussed too.
