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This paper introduces an original multi-resolution 3D mesh compression technique, called Shape Approximation-based Progressive Mesh (SAPM). The proposed approach losslessly compresses the mesh connectivity and exploits it in order to build a smooth approximation of the original mesh. The obtained mesh approximation is then decimated yielding a progressive mesh hierarchy. This hierarchy is used to efficiently predict and progressively transmit the geometry approximation errors. The proposed codec supports both spatial and quality scalabilities and offers high rate-distortion performances. Experimental evaluation shows that the SAPM codec is on average 38-57% more efficient than the state-of-the-art connectivity preserving 3D mesh compression techniques.