While block copolymer lithography has been broadly applied as a bottom-up patterning technique, only a few nanopattern symmetries, such as hexagonally packed dots or parallel stripes, can be produced by spontaneous self-assembly of simple diblock copolymers; even a simple square packing has heretofore required more intricate macromolecular architectures or nanoscale substrate prepatterning. In this study, we demonstrate that square, rectangular, and rhombic arrays can be created via shear-alignment of distinct layers of cylinder-forming block copolymers, coupled with cross-linking of the layers using ultraviolet light. Furthermore, these block copolymer arrays can in turn be used as templates to fabricate dense, substrate-supported arrays of nanostructures comprising a wide variety of elements: deep (>50 nm) nanowells, nanoposts, and thin metal nanodots (3 nm thick, 35 nm pitch) are all demonstrated