  In the framework of certain general probability theories of single systems,
we identify various nonclassical features such as incompatibility, multiple
pure-state decomposability, measurement disturbance, no-cloning and the
impossibility of certain universal operations, with the non-simpliciality of
the state space. This is shown to naturally suggest an underlying simplex as an
ontological model. Contextuality turns out to be an independent nonclassical
feature, arising from the intransitivity of compatibility.
