A new mesh simplification framework based on the i®simplex collapse', which can produce approximations of simplified complexes of any type of meshes embedded in three dimensional Euclidean spaces, such as triangular meshes, quadrangular meshes, tetrahedral meshes, hexahedral meshes, and mixed complexes was presented in this paper. It has higher decimations ratio than the i®edge collapse'-based methods. We described the general process of the general mesh simplification and its data structure and operations prototypes. Having different prey rule and reconstruction rules, this framework can reduce the general mesh dataset rapidly and effectively. The general mesh simplification algorithm has been applied to the three dimensional geological modeling. Additionally, this framework can be extended to multi-dimensions (>3) spaces.