of the triangles of the lattice. Hence one of the sublattices is distinguished from the others. At low particle density the probability for a particle to be on a particular site is equal for sites on all three sublattices (assuming either an infinite or sufficiently large lattice so that boundary effects can be neglected). Let $\rho_a$ for $a=1,2,3$ be the probability that there is a particle at a fixed site on sublattice $1,2,3$, respectively. If the boundary conditions of the model are such that at close packing all particles are on sublattice 1 then it is intuitively clear that the order parameter defined as $R=\rho_1-\rho_2$ must undergo a phase transition. At low densities $R$ is zero, but at some critical density $R$ will become positive until at high densities it is one. Baxter [@B81] managed to determine the precise point at which the phase transition occurs exactly by using corner transfer matrices. In essence, the corner transfer matrix method reduces the two-dimensional problem to a one-dimensional problem. The precise details are beyond the scope of this paper and can be found in section 14 of Baxter’s book [@B82].

The one-dimensional problem that Baxter encountered and which turns out to be 