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In this paper, we consider the problem of representing a multiresolution geometric model, called a Simplicial Multi-Complex (SMC), in a compact way. We present encoding schemes for both two-an d threedimensional SMCs built through a vertex insertion (removal) simplification strategy. We show that a good compression ratio is achieved not only with respect to a general-purpose data structure for a SMC, but also with respect to just encoding the complex at the maximum resolution.