This ice model provide an important 'counterexample' in statistical mechanics: the bulk free energy in the thermodynamic limit depends on boundary conditions. The model was analytically solved for periodic boundary conditions, anti-periodic, ferromagnetic and domain wall boundary conditions. The six vertex model with domain wall boundary conditions on a square lattice has specific significance in combinatorics, it helps to enumerate alternating sign matrices. In this case the partition function can be represented as a determinant of a matrix (whose dimension is equal to the size of the lattice), but in other cases the enumeration of W does not come out in such a simple closed form.