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The various proposed DHT routing algorithms embody several different underlying routing geometries. These geometries include hypercubes, rings, tree-like structures, and butterfly networks. In this paper we focus on how these basic geometric approaches affect the resilience and proximity properties of DHTs. One factor that distinguishes these geometries is the degree of flexibility they provide in the selection of neighbors and routes. Flexibility is an important factor in achieving good static resilience and effective proximity neighbor and route selection. Our basic finding is that, despite our initial preference for more complex geometries, the ring geometry allows the greatest flexibility, and hence achieves the best resilience and proximity performance.