  Crystalline assemblages of identical sub-units packed together and
elastically bent in the form of a torus have been found in the past ten years
in a variety of systems of surprisingly different nature, such as viral
capsids, self-assembled monolayers and carbon nanomaterials. In this Letter we
analyze the structural properties of toroidal crystals and we provide a unified
description based on the elastic theory of defects in curved geometries. We
find ground states characterized by the presence of 5-fold disclinations on the
exterior of the torus and 7-fold disclinations in the interior. The number of
excess disclinations is controlled primarily by the aspect ratio of the torus,
suggesting a novel mechanism for creating toroidal templates with precisely
controlled valency via functionalization of the defect sites.
