Intrinsic dynamics of the central vestibular system (CVS) appear to be at least partly determined by the symmetries of its connections. The CVS contributes to whole-body functions such as upright balance and maintenance of gaze direction. These functions coordinate disparate senses (visual, inertial, somatosensory, auditory) and body movements (leg, trunk, head/neck, eye). They are also unified by geometric conditions. Symmetry groups have been found to structure experimentally-recorded pathways of the central vestibular system. When related to geometric conditions in three-dimensional physical space, these symmetry groups make sense as a logical foundation for sensorimotor coordination.