  Symplectic (respectively orthogonal) triple systems provide constructions of
Lie algebras (resp. superalgebras). However, in characteristic 3, it is shown
that this role can be interchanged and that Lie superalgebras (resp. algebras)
can be built out of symplectic triple systems (resp. orthogonal triple systems)
with a different construction. As a consequence, new simple finite dimensional
Lie superalgebras, as well as new models of some nonclassical simple Lie
algebras, are obtained over fields of characteristic 3.
