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Motivated by the existence of two frequency bands and inspired from Lie algebra classification, the authors propose a new geometric cellular shape with double hexagonal structure. Based on a two dimensional root system of the exceptional Lie algebra G2, this cellular network model involves two hexagons of unequal side length at angle 30Degree. In this new hexagonal cellular networks, the principal hexagonal unit cell contains twelve coverage limits in contrast of the usual structure involving only six ones. Within the G2 hexagonal structure, two frequency bands can be now placed at the same sheet in contrast to the single hexagonal structure where it can appear only one frequency band.
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