Symmetric cellular network embeddings on a torus

Infinite planar cellular networks are embedded on a torus to obtain a symmetric regular finite network sample region for performance analysis. We show that a “hexagonal wrap” toroidal embedding preserves translational and rotational symmetry on all three axes of a hexagonal lattice and is preferable to a “Cartesian wrap” embedding. Hexagonal tilings and embeddings are obtained for all rhombic tile sizes. Certain tilings are shown to provide modular based neighbor addressing schemes that simplify distributed channel assignment algorithms. Hierarchical “hexagons within a hexagon” tilings are illustrated with the large hexagon exhibiting the sample repeat and comprising a multiplicity of channel frequency repeat small hexagonal the clusters. The symmetric hexagonal sample region repeat embeddings are noted to be useful for probabilistic analysis of high utilization channel assignment performance both theoretically and by simulation