  Toroidal templates such as vesicles with hexatic bond orientational order are
discussed. The total energy including disclination charges is explicitly
computed for hexatic order embedded in a toroidal geometry. Related results
apply for tilt or nematic order on the torus in the one Frank constant
approximation. Although there is no topological necessity for defects in the
ground state, we find that excess disclination defects are nevertheless
energetically favored for fat torii or moderate vesicle sizes. Some
experimental consequences are discussed.
