The integrability condition of three-dimensional exactly solvable model-Baxter-Bazhanov model in statistical mechanics

From the chiral Potts model the 'inversion' and 'star-square' relations of the Baxter-Bazhanov model are obtained. This means that the tetrahedron equation which is a commutativity condition for the three-dimensional cubic lattice is a consequence of the star-triangle relation of the chiral Potts model. The additional constraints in tetrahedron equation hold naturally when the Boltzmann weights are parametrized in terms of the Zamolodchikov angle variables. It is point out that the star-triangle relation of the three-dimensional model can be gotten by using the method given in this paper, which includes the result of Baxter and Bazhanov's. (authors)