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Аннотация We present a theory of the photonic band structure of three-dimensional arrays of quantum dots (QDs). A system of Maxwell and material equations is solved and the dispersion equation for exciton polaritons is derived making allowance for a nonlocal dielectric response of quasi-zero-dimensional excitons confined in QDs. The reflection and transmission coefficients are calculated for a single plane, a pair of planes and a stack of equidistant planes of QDs. Two different approaches are proposed to perform the calculation. One of them is based on recurrent equations relating the reflection coefficients for N+1 and N planes, and in other approach the Bloch solutions for an infinite QD lattice are used. E.L.I. would like to thank the program "Nanostructures" (Russian Ministry of Science) and Russian Foundation for Basic Research for financial support.