The ability to form a square array is particularly significant for applications in patterning and templating, allowing for instance compatibility with the rectilinear architectures that are critical to integrated circuits including in memory storage and bit-patterned media. Such symmetry is hard to achieve in self-assembled 2D systems, where hexagonal arrays are much more common. In block copolymer systems, approaches where the square array is achieved through constraints in topologically patterned substrates have realized periodicity as low as 27 nm. For unconstrained systems that spontaneously adopt square arrays, as in the current work, triblock and supramolecular copolymer systems have periodic repeats of 40-50 nm, over three times larger than those reported here. In bit-patterned media, the bit density is inversely proportional to the square of the repeat spacing; our work therefore has the potential to achieve almost an order of magnitude increase in storage density.