  We show how OSp(1|32) gives a unifying framework to describe d=10 type II
string theories, d=11 M-theory and d=12 F-theory. The theories are related by
different identifications of their symmetry operators as generators of
OSp(1|32). T- and S-dualities are recognized as redefinitions of generators.
Some (s,t) signatures of spacetime allow reality conditions on the generators.
All those that allow a real structure are related again by redefinitions within
the algebra, due to the fact that the algebra OSp(1|32) has only one real
realization. The redefinitions include space/space, time/time and space/time
dualities. A further distinction between the theories is made by the
identification of the translation generator. This distinguishes various
versions of type II string theories, in particular the so-called *-theories,
characterized by the fact that the P_0 generator is not the (unique)
positive-definite energy operator in the algebra.
