  Duality relations for the 2D nonhomogeneous Ising model on the finite square
lattice wrapped on the torus are obtained. The partition function of the model
on the dual lattice with arbitrary combinations of the periodical and
antiperiodical boundary conditions along the cycles of the torus is expressed
through some specific combination of the partition functions of the model on
the original lattice with corresponding boundary conditions. It is shown that
the structure of the duality relations is connected with the topological
peculiarities of the dual transformation of the model on the torus.
