  We study the partition function for the three-colour model with domain wall
boundary conditions. We express it in terms of certain special polynomials,
which can be constructed recursively. Our method generalizes Kuperberg's proof
of the alternating sign matrix theorem, replacing the six-vertex model used by
Kuperberg with the eight-vertex-solid-on-solid model. As applications, we
obtain some combinatorial results on three-colourings. We also conjecture an
explicit formula for the free energy of the model.
