A model ternary polymer mixture is considered with bi- and tri-functio
nal monomers and a solvent embedded on a honeycomb lattice. The model
is shown to be equivalent to an eight-vertex model on the same lattice
. Using this equivalence which further maps the problem into an Ising
model in a non-zero magnetic field, an exact analysis of the model is
carried out. The two phase coexistence surface in the temperature-comp
osition space is determined exactly and connectivity properties of the
model are studied.