Three-dimensional (3D) photonic crystals are made up of position-dependent dielectric materials with periodic structures. In the previous research, we first use the Yee’s finite difference scheme to discretize the double curl operator. This procedure of discretize is highly related to quasi-periodic conditions of lattice structure, so to study the structure of lattice is necessary. Crystals in 3D Euclidean space can be classified into 14 Bravais lattices. So far, we have developed the fast solver about the simple cubic and the face-centered cubic lattices, we hope to extend the same technique to other twelve Bravais lattices in the future. In this talk, I will briefly introduce some knowledges crystallography, include: some common crystal structure, Miller index, Miller-Bravais index and Stereographic projections. Then, I will introduce the symmetry of the crystals in detail.