Finding locations in a familiar environment requires accurate representations of space (‘cognitive maps’). In many species, the neural basis of cognitive maps are a set of specialized neurons in the hippocampal formation. Previous research has found that stretching or squashing environmental dimensions alters the firing pattern of hippocampal place cells and entorhinal grid cells in freely moving rodents as well as human spatial memory. This Indicates that boundaries defining the geometry of space play an important role in determining the nature of cognitive maps. Here, we examined how behavioural changes to environmental deformations relate to those on a neural level as measured with functional magnetic resonance imaging (fMRI) in humans, and how these effects can be explained by models of cellular firing. In this two-day study, we first trained participants to learn the location of objects inside a virtual arena. During subsequent scanning, we asked them to re-visit each location inside the arena as well as actively imagine them outside the arena. Critically, the arena deformed from square to rectangular shape across days. So far, we found shifts in spatial memory related to the change in geometry that is best explained by a model of neurons sensitive to boundaries (‘boundary vector cells’, BVC). Furthermore, our fMRI data suggest that the hippocampus may use a distance code to represent the relationship between locations that scales with the geometry of the environment. Our study extends our understanding of how the cognitive map anchors its spatial representation to the external world.