With the aid of numerical simulations, we study the tunability of photonic structures by evidencing the band gaps (BGs) of two interesting particular hexagonal and triangular photonic crystals. Several runs were performed for different values of the dielectric constant ranging from ε = 15 to ε = 150. Results showed that the BGs cover large intervals. The numerical model used for the simulations is presented. We conclude these configurations could be used for a tunable high-reflectivity and high-directionality antenna. The analogy between electronic waves in the crystal and light waves in a three-dimensionally periodic structure and the evidencing of a complete photonic band gap led to further studies, which cover a large range of domains.