Photonic crystals, artificial microstructures composed of periodic dielectric materials, have broad application prospects in integrated optoelectronics, nanophotonics, and other fields. In this paper, the fabrication of compound photonic crystals by the multi-beam holographic interferometry is studied theoretically and numerically. According to the multi-beam interference principle, we design a beam configuration of compound photonic crystals and write a program by MATLAB. The simulation results agree well with the theoretical predictions. Furthermore, we symmetrically study the influences of single-beam, two-beam, three-beam, and four-beam polarization combinations on the unit cell of the compound photonic crystals. The results indicate that polarization combinations have a significant influence on the unit cell, and various unit-cell shapes such as double-drop and double-circle shapes can be easily obtained at different polarization combinations. The optimal contrast is achieved when all beams are linear polarization. Additionally, the influence of the initial phase of the incident light on the unit cell is discussed. The above research guides the design and fabrication of compound photonic crystals with various unit-cell shapes and can be used in the physics experiment teaching.