It has long been known that ice nucleation usually proceeds heterogeneously on the surface of a foreign body. However, little is known at the microscopic level about which properties of a material determine its effectiveness at nucleating ice. This work focuses on the long standing, conceptually simple, view on the role of a good crystallographic match between bulk ice and the underlying substrate. We use grand canonical Monte Carlo to generate the first overlayer of water at the surface and find that the traditional view of heterogeneous nucleation does not adequately account for the array of structures that water may form at the surface. We find that, in order to describe the structures formed, a good match between the substrate and the nearest neighbour oxygen–oxygen distance is a better descriptor than a good match to the bulk ice lattice constant.