The mammalian hippocampal formation provides neuronal representations of environmental location, but the underlying mechanisms are poorly understood. Here, we report a class of cells whose spatially periodic firing patterns are composed of plane waves (or bands) drawn from a discrete set of orientations and wavelengths. The majority of cells recorded in parasubicular and medial entorhinal cortices of freely moving rats belonged to this class and included grid cells, an important subset that corresponds to three bands at 60 orientations and has the most stable firing pattern. Occasional changes between hexagonal and nonhexagonal patterns imply a common underlying mechanism. Our results indicate a Fourier-like spatial analysis underlying neuronal representations of location, and suggest that path integration is performed by integrating displacement along a restricted set of directions.