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One- and two-dimensional photonic crystals based on silicon with infiltrated liquid crystals are investigated in this paper. We show that the photonic band gap can be continuously tuned changing the orientation of the director of the liquid crystal. For the one-dimensional case, we considered arbitrary direction of propagation of the electromagnetic waves, and we show that it is possible to tune the photonic band gap by an adequate orientation of the liquid crystal. For the two-dimensional case and propagation in the plane of periodicity, we show that there exists no complete photonic band gap in the system for both polarizations. We consider two different configurations, square array of solid Si cylinders in liquid crystal background and a triangular array of liquid crystal cylinders surrounded by Si. We show that for the triangular array it is possible to tune the photonic band gap only for the transversal electric modes. We used the plane wave expansion method to solve the Maxwell equations for anisotropic systems.