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The recent growth in the size and availability of large triangularsurface models has generated interest in compactmulti-resolution progressive representation and data transmission.An ongoing challenge is to design an efficient datastructure that encompasses both compactness of geometricrepresentations and visual quality of progressive representations.In this paper we introduce a topological layering baseddata-structure and an encoding scheme to build a compactprogressive representation of an arbitrary triangular mesh (a2D simplicial complex in 3D) with attached attribute data.This compact representation is composed of multiple levelsof detail that can be progressively transmitted and displayed.The global topology, which is the number of holesand connected components, can be flexibly changed amongsuccessive levels while still achieving guaranteed size of thecoarsest level mesh for very complex models. The flexibilityin our encoding scheme also allows topology preservingprogressivity.