As a new type of sandwich structure, regular polyhedron sandwich structure has excellent structure performances such as high bending resistance and energy-absorbing features. However, the current design process of regular polyhedron sandwich structures often ignores the influence of unit-cell parameters on structural bending stiffness. Based on origami geometry, this study analyzes the geometric characteristics of polyhedron unit-cell structures. A simulation model was established to analyze the bending performance of regular polyhedron sandwich structures. The influence of the number of polyhedron surfaces and similarity transformation parameters on bending stiffness was analyzed by finite element software. Through finite simulation analysis, the influence graph of bending performance in the impact of various parameters was obtained. This analysis provides valuable insights for the optimization design of regular polyhedron sandwich structures.