When a photon is absorbed by a group of identical chromophores the excited state may be described as an exciton. Such excitons play a significant role in the energetics of many photoactive systems, and in particular the photosynthetic unit. This work concerns the transfer of excitonic energy to a donor, focussing on the effects of geometry. To facilitate the analysis, calculated quantum amplitudes are expressed in terms of orientation factors with clear physical significance. In detailed calculations on an idealised, three-fold symmetric photosystem it is shown that intermolecular vectors and relative transition dipole moment orientations directly affect transfer rates, and the detailed form of that dependence is determined. Differences in the linear combinations which form the excitonic states are fully investigated and various configurations exclusively exhibiting excitonic behaviour are identified.