The authors consider the duality properties of a general vertex model on a lattice in any spatial dimension. The analysis is based on a generalised weak-graph transformation under which the partition function of the vertex model remains invariant. It is shown that the generalised weak-graph transformation is self-dual for lattice coordination number q=2, 3, 4, 5, 6, and they conjecture that the self-dual property holds for general q. They also obtain the self-dual manifold for q=3, 4, and it is found that, in an Ising subspace, the manifold coincides with the known Ising critical locus.