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The fundamental and natural connection between the infinite constellation (IC) dimension and the best diversity order it can achieve is investigated in this paper. In the first part of this work we develop an upper bound on the diversity order of IC for any dimension and any number of transmit and receive antennas. In the second part of this work we prove that by choosing the correct dimensions, IC in general and lattices in particular can achieve the optimal diversity-multiplexing tradeoff of finite constellations. This work gives a framework for designing lattices for multiple-antenna channels using lattice decoding.