An intriguing observation of photosynthetic light-harvesting systems is the N-fold symmetry of light-harvesting complex 2 (LH2) of purple bacteria. We calculate the optimal rotational configuration of N-fold rings on a hexagonal lattice and establish two related mechanisms for the promotion of maximum excitation energy transfer (EET). (i) For certain fold numbers, there exist optimal basis cells with rotational symmetry, extendable to the entire lattice for the global optimization of the EET network. (ii) The type of basis cell can reduce or remove the frustration of EET rates across the photosynthetic network. We find that the existence of a basis cell and its type are directly related to the number of matching points S between the fold symmetry and the hexagonal lattice. The two complementary mechanisms provide selection criteria for the fold number and identify groups of consecutive numbers. Remarkably, one such group consists of the naturally occurring 8-, 9-, and 10-fold rings. By considering the inter-ring distance and EET rate, we demonstrate that this group can achieve minimal rotational sensitivity in addition to an optimal packing density, achieving robust and efficient EET. This corroborates our findings i and ii and, through their direct relation to S, suggests the design principle of matching the internal symmetry with the lattice order.P hotosynthesis lies at the heart of all life on the planet. Excitation energy created in a peripheral light-harvesting antenna complex, upon absorption of a photon, is efficiently transferred via an exciton mechanism, sometimes over hundreds of angstroms, to a reaction center where charge separation takes place, creating a transmembrane electrochemical potential difference that ultimately drives the production of ATP. Light-harvesting antenna complexes, whose primary function is to increase the effective crosssection for photon absorption, while maintaining an efficient energy transfer network, consist of well-ordered membrane-associated arrays of light-absorbing pigments, namely chlorophyll or bacterichlorophyll (BChl), embedded in a protein environment (1-4).Perhaps the most intriguing aspect of light-harvesting systems is the N-fold symmetry displayed by light-harvesting complex 2 (LH2) of purple nonsulfur bacteria. Fold symmetry occurs in systems as diverse as carbon nanotubes, tubular dye aggregates, and the mosaic virus protein, as well as in snow flakes, tori, and nonperiodic tilings (5). In LH2, the N-fold symmetry arises from the N repetitions of a basic heterodimer subunit consisting of two transmembrane polypeptides, α and β, arranged in a circular structure (6-8). Each αβ-heterodimer subunit noncovalently binds one B800 BChl and two B850 BChls (Fig. 1A), so named according to their respective room-temperature absorption bands in the infrared region of the spectrum. In most bacterial species, the αβ-heterodimer repeats eight or nine times to form an octameric or nonameric ring structure (in Rhodopseudomonas paulisterium 10-fold rings have also been observ...