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Traditional approaches to constructing constellations for electrical channels cannot be applied directly to the optical intensity channel. This work presents a structured signal space model for optical intensity channels where the nonnegativity and average amplitude constraints are represented geometrically. Lattice codes satisfying channel constraints are defined and coding and shaping gain relative to a baseline are computed. An effective signal space dimension is defined to represent the precise impact of coding and shaping on bandwidth. Average optical power minimizing shaping regions are derived in some special cases. Example lattice codes are constructed and their performance on an idealized point-to-point wireless optical link is computed. Bandwidth-efficient schemes are shown to have promise for high data-rate applications, but require greater average optical power.