There have been suggestions that human navigation may depend on representations that have no metric, Euclidean interpretation but that hypothesis remains contentious. An alternative is that observers build a consistent 3D representation of space. Using immersive virtual reality, we measured the ability of observers to point to targets in mazes that had zero, one or three 'wormholes' regions where the maze changed in configuration (invisibly). In one model, we allowed the configuration of the maze to vary to best explain the pointing data; in a second model we also allowed the local reference frame to be rotated through 90, 180 or 270 degrees. The latter model outperformed the former in the wormhole conditions, inconsistent with a Euclidean cognitive map.