  The duality relation for the effective conductivity sigma_{e} of 2D isotropic
heterophase systems is used for obtaining the exact results for sigma_{e} at
arbitrary number of phases N. The exact values of sigma_{e} correspond to the
fixed points of the duality transformations. The new exact results for
sigma_{e}, generalizing the well-known exact values of sigma_{e} for N = 2,3 at
equal phase concentrations, are found. It is shown that for N > 3 there exist
the whole hyperplanes in the space of phase concentrations, on which sigma_{e}
takes constant values. These results are checked in the framework of various
approximations for different random heterophase systems.
