Abstract: Two rules to define and search the n-edges-mesh (‘n’ is a positive integer ) in triangle meshes are presented and a new mesh simplification algorithm based on the n-edges-mesh collapse is put forward, which has the same law of collapse in different n cases. The proposed algorithm utilizes iterative n-edges-mesh collapse to simplify meshes. Surface error approximations are maintained using quadric errors metrics. There are n-1 vertices and 2n-2 faces to be collapsed during every simplification, so fewer collapses times are need to reach a target simplified model with a certain number of triangles when n is assigned a relatively large value. And that means the time of the simplification process can be reduced. Furthermore, by choosing the proper ‘n’ and the position of the new vertex, the new algorithm can be transformed into the known geometry element collapse (remove) algorithm which is based on the vertex decimation process, the edge collapse process, or the triangle collapse process. Thus the proposed algorithm can be regarded as the summarized algorithm of mesh simplification based on the geometry element collapse. Different n cases are involved in the experiment, and the results demonstrate the efficiency of the algorithm.