We show here that the boundaries of individual grains in dense polycrystals prefer certain crystallographic habit planes, almost as if they were independent of the neighboring crystals. In MgO, SrTiO3, MgAl2O4, TiO2, and aluminum, the specific habit planes within the polycrystal correspond to the same planes that dominate the external growth forms and equilibrium shapes of isolated crystals of the same phase. The observations decrease the apparent complexity of interfacial networks and suggest that the mechanisms of solid-state grain growth may be analogous to conventional crystal growth. The results also indicate that a model for grain-boundary energy and structure based on grain surface relationships is more appropriate than the widely accepted models based on lattice orientation relationships.