It has long been appreciated that liquid-crystal (LC) devices in which the LC molecules adopt multiple stable orientations could drastically reduce the power consumption required for high-information-content displays. But for the commonly used nematic LCs, which are intrinsically uniaxial in symmetry, no industrially feasible multi-stable LC device has been realized. Recently we demonstrated how bistability can be robustly engineered into a nematic LC device, by patterning a substrate with an orientational chequerboard pattern that enforces orthogonal LC alignment in neighbouring square domains. As a result of the four-fold symmetry of the pattern, the two diagonal axes of the chequerboard become equally stable macroscopic orientations. Here we extend this symmetry approach to obtain a tristable surface-aligned nematic LC. A microscopic pattern exhibiting six-fold symmetry is inscribed on a polyimide surface using the stylus of an atomic force microscope. The hexagonal symmetry of the microscopic orientational domains in turn gives rise to three stable macroscopic LC orientations, which are mutually switchable by an in-plane electric field. The resulting switching mode is surface driven, and hence should be compatible with demanding flexible display applications.