Using electron microscopy, we identify local, intergranular regions of hexagonal close-packing at a grain boundary in gold. By analyzing the topological defects that connect this layer to the adjacent face-centered cubic grains, we explain the geometric origin of this interfacial reconstruction. We extend this analysis to predict the stacking arrangements found over a range of intergranular misorientations. These results help to unify our understanding of the defects that control the behavior of polycrystalline materials by showing how line defects that are already well understood in the bulk also can determine the atomic arrangements at grain boundaries.