In this paper, we consider the method of partitioning a sphere into faces with a set of spherical convex polygons $Gamma$=$｛P_1...P_n｝$ for determining the maximum of minimum intersection. This problem is commonly related with five geometric problems that fin the densest hemisphere containing the maximum subset of $Gamma$, a great circle separating $Gamma$, a great circle bisecting $Gamma$ and a great circle intersecting the minimum or maximum subset of $Gamma$. In order to efficiently compute the minimum or maximum intersection of spherical polygons. we take the approach of edge-based partition, in which the ownerships of edges rather than faces are manipulated as the sphere is incrementally partitioned by each of the polygons. Finally, by gathering the unordered split edges with the maximum number of ownerships. we approximately obtain the centroids of the solution faces without constructing their boundaries. Our algorithm for finding the maximum intersection is analyzed to have an efficient time complexity O(nv) where n and v respectively, are the numbers of polygons and all vertices. Furthermore, it is practical from the view of implementation, since it computes numerical values. robustly and deals with all the degenerate cases, Using the similar approach, the boundary of a general intersection can be constructed in O(nv+LlogL) time, where : is the output-senstive number of solution edges.