  In this article we consider a generalization of manifolds and orbifolds which
we call quasifolds; quasifolds of dimension k are locally isomorphic to the
quotient of R^k by the action of a discrete group - tipically they are not
Hausdorff topological spaces. The analogue of a torus in this geometry is a
quasitorus. We define Hamiltonian actions of quasitori on symplectic quasifolds
and we show that any simple convex polytope, rational or not, is the image of
the moment mapping for a family of effective Hamiltonian actions on symplectic
quasifolds having twice the dimension of the corresponding quasitorus.
