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This paper introduces a novel scalable 3D mesh compression technique based on a shape approximation prediction strategy. The proposed approach, so-called Shape Approximation Compression (SAC), directly compresses the levels of detail (LoDs) defined by the content creators, while exploiting their inter-correlations. Here, the geometry of each LoD is used in order to compute a smooth approximation of the next layer. A progressive mesh hierarchy is then built on the top of the approximated version making it possible to efficiently predict and progressively transmit the geometry approximation errors. The SAC codec was evaluated within the framework of the MPEG core experiments on Multi-Resolution 3D Mesh Coding (MR3DMC) and was preliminarily accepted for future standardization.