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In computer graphics, object are often represented by triangle meshes. Iterative collapse of geometric elements is an important way to simplify the meshes. This paper presents a method for dividing the triangle mesh into certain kind of multi-edge mesh and puts forward a new mesh simplification algorithm based on the multi-edge mesh collapse. The algorithm utilizes iterative collapse of multi-edge mesh to simplify meshes and the surface error approximations are maintained using quadric error metrics. A multi-edge mesh containing n exterior edges, and during every simplification, 2(n-1) faces are collapsed, so much less collapses are need when n becomes bigger. In many cases, the time of the simplification process can be reduced.