Numerical simulation of the TM modes dispersion relation and optical bandgaps found in a triangular lattice of cylindrical air holes in 4H-SiC. The normalized frequency is plotted as a function of the in plane photon wave vector considered. The horizontal axis indicates the in plane wavevector of the photon, along the direction Γ K, K M, and M Γ. Parameters: refractive index n_air = 1, n_SiC = 2.5 and r = 0.29 × a, with r the radius of air holes and a the inter-center distance between neighbor air holes in the triangular lattice.