Grid cell symmetry is shaped by environmental geometry.

Grid cells represent an animal's location by firing in multiple fields arranged in a striking hexagonal array. Such an impressive and constant regularity prompted suggestions that grid cells represent a universal and environmental-invariant metric for navigation. Originally the properties of grid patterns were believed to be independent of the shape of the environment and this notion has dominated almost all theoretical grid cell models. However, several studies indicate that environmental boundaries influence grid firing, though the strength, nature and longevity of this effect is unclear. Here we show that grid orientation, scale, symmetry and homogeneity are strongly and permanently affected by environmental geometry. We found that grid patterns orient to the walls of polarized enclosures such as squares, but not circles. Furthermore, the hexagonal grid symmetry is permanently broken in highly polarized environments such as trapezoids, the pattern being more elliptical and less homogeneous. Our results provide compelling evidence for the idea that environmental boundaries compete with the internal organization of the grid cell system to drive grid firing. Notably, grid cell activity is more local than previously thought and as a consequence cannot provide a universal spatial metric in all environments.