Information about discrete objects in the environment is encoded by neurons of the lateral entorhinal cortex using vector information of the objects in relation to other items or boundaries. The neurons encoding the space between objects are unknown. Here, neurons in the medial entorhinal cortex, termed ‘object vector cells’, were found to encode distances and directions from discrete objects, that is, they use allocentric vector coding to represent items in the test arena. These findings provide a cellular basis for position mapping in the space between objects.