Is Pauling's hypothesis violated in the hexagonal modification of ice?

The effect of long-range dipole interaction on the fulfilment of Pauling’s hypothesis concerning the degeneracy of proton configurations satisfying the ice rules is studied for the case of hexagonal ice. It is shown that the ice rules imply a significant reduction of the contributions to the ground state energy from the next-nearest neighbors. The ground state energy of proton subsystem as a function of quasimomentum ceases to change if more than a hundred primitive unit cells in each direction are taken into account. The final amplitude of the energy changes are about 70 K. The analysis reveals the proton ordering in hexagonal ice with the simple unit cell of the oxygen sublattice is impossible. However, that does not exclude proton ordering with a more complex cell caused by distortion of the hexagonal oxygen lattice.