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Efficient algorithms for compressing three-dimensional (3D) triangle meshes have been widely developed in recent years, but most of them are designed to deal with manifold meshes. A progressive geometry-driven 3D triangle meshes algorithm is proposed in this work which can be easily extended to non-manifold mesh compression and polygon mesh compression. Different from connectivity-driven algorithms; our method starts with the geometry; it encodes the geometry data into a symbol sequence consisting of only three kinds of symbols. Edge collapse and vertex unification operator are used to encode the connectivity, and the symbol sequences can be further encoded by arithmetic coding.