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Generating laterally ordered, ultradense, macroscopic arrays of nanoscopic elements will revolutionize the microelectronic and storage industries. We used faceted surfaces of commercially available sapphire wafers to guide the self-assembly of block copolymer microdomains into oriented arrays with quasi–long-range crystalline order over arbitrarily large wafer surfaces. Ordered arrays of cylindrical microdomains 3 nanometers in diameter, with areal densities in excess of 10 terabits per square inch, were produced. The sawtoothed substrate topography provides directional guidance to the self-assembly of the block copolymer, which is tolerant of surface defects, such as dislocations. The lateral ordering and lattice orientation of the single-grain arrays of microdomains are maintained over the entire surface. The approach described is parallel, applicable to different substrates and block copolymers, and opens a …