The freezing of water typically proceeds through impurity-mediated heterogeneous nucleation. Although non-planar geometry generically exists on the surfaces of ice nucleation centres, its role in nucleation remains poorly understood. Here we show that an atomically sharp, concave wedge can further promote ice nucleation with special wedge geometries. Our molecular analysis shows that significant enhancements of ice nucleation can emerge both when the geometry of a wedge matches the ice lattice and when such lattice match does not exist. In particular, a 45° wedge is found to greatly enhance ice nucleation by facilitating the formation of special topological defects that consequently catalyse the growth of regular ice. Our study not only highlights the active role of defects in nucleation but also suggests that the traditional concept of lattice match between a nucleation centre and crystalline lattice should be extended to include a broader match with metastable, non-crystalline structural motifs.