The subjective sense of space may result in part from the combined activity of place cells in the hippocampus and grid cells in posterior cortical regions such as the entorhinal cortex and pre- and parasubiculum. In horizontal planar environments, place cells provide focal positional information, whereas grid cells supply odometric (distance measuring) information. How these cells operate in three dimensions is unknown, even though the real world is three-dimensional. We investigated this issue in rats exploring two different kinds of apparatus: a climbing wall (the 'pegboard') and a helix. Place and grid cell firing fields had normal horizontal characteristics but were elongated vertically, with grid fields forming stripes. It seems that grid cell odometry (and by implication path integration) is impaired or absent in the vertical domain, at least when the rat itself remains horizontal. These findings suggest that the mammalian encoding of three-dimensional space is anisotropic.