Abstract: The fundamental concepts and definitions of polyhedra and set operations tare discussed in this paper. Based on the concepts and B-Rep definitions, the paper will make great efforts to study the process of evaluating intersections between two faces without co-line edges, and partitioning the loops on the faces. The algorithm of partitioning loops is proposed and its three key steps are presented in detail: (1) The consistent mapping from solid A to solid AA, (2) the evaluation and classification of intersecting-line edges, (3) the calculating process of simple-loop partition and sophisticated-loop partition. Finally, the experimentell results of the algorithm are concluded.