Atomically smooth hexagonal boron nitride (h-BN) films are considered as a nearly ideal dielectric interface for two-dimensional (2D) heterostructure devices. Reported mono- to few-layer 2D h-BN films, however, are mostly small grain-sized, polycrystalline and randomly oriented. Here we report the growth of centimetre-sized atomically thin h-BN films composed of aligned domains on resolidified Cu. The films consist of monolayer single crystalline triangular and hexagonal domains with size of up to ∼10 μm. The domains converge to symmetrical multifaceted shapes such as “butterfly” and “6-apex-star” and exhibit ∼75% grain alignment for over millimetre distances as verified through transmission electron microscopy. Scanning electron microscopy images reveal that these domains are aligned for over centimetre distances. Defect lines are generated along the grain boundaries of mirroring h-BN domains due to the two different polarities (BN and NB) and edges with the same termination. The observed triangular domains with truncated edges and alternatively hexagonal domains are in accordance with Wulff shapes that have minimum edge energy. This work provides an extensive study on the aligned growth of h-BN single crystals over large distances and highlights the obstacles that are needed to be overcome for a 2D material with a binary configuration.