The basic elements and characteristics of Archimedean polyhedron composition were analyzed, which was frequently used in packaging design. Two kinds of connection between the two composition units were discussed. Multiple elements primary equation set was established and quaternary mathematical expression of shape and quantity of the composition unit was solved. The feasibility of multivariate equations was verified with the composition manner of 14, 26 and 32 sides of Archimedean polyhedron. The shape and quantity of the composition elements in actual design process was solved. The purpose was to provide more practical theoretical basis for designer.