Corner transfer matrices of the chiral Potts model. II. The triangular lattice

We consider a two-dimensional edge-interaction model satisfying the star-triangle relations. For the triangular lattice, the corner transfer matrices are functions of three rapidities: we show that they possess various factorization properties and satisfy certain equations. We indicate how these equations can be solved for the Ising model. We then consider the three-state chiral Potts model and obtain low-temperature solutions to the equations. The conjectured formula for the order parameter (the spontaneous magnetization) is verified to one more order in a series expansion.