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The 2D hexagonal mesh, based on triangle plane tessellation, is considered as a multiprocessor interconnection network. The 3D hexagonal mesh is presented as a natural extension of the hexagonal mesh. Although the topological properties of the 2D hexagonal mesh are well known, existing addressing schemes are not suitable to be extended to 3D hexagonal mesh. Then, we present, in this paper, a new addressing scheme and an optimal routing algorithm for 2D hexagonal network based on the distance formula and using shortest paths. We propose also a 3D hexagonal network that can be built with 2D hexagonal meshes as a natural generalization. We also present some topological properties, an efficient addressing scheme, and an optimal routing algorithm based on our 2D routing algorithm.