The OREGAMI project seeks to develop algorithms and abstractions for mapping parallel algorithms to message-passing machines when both the computation and the interconnection network are regular in structure. In collaboration with Sanjay Rajopadhye of IRISA, France, we have developed a formalism for describing both the computation and the target architecture which aids in the development of efficient and effective mapping functions. This approach exploits regularity in both the spatial and temporal communication patterns exhibited by many parallel applications.