1 Motivation Current multiresolution and topology-preserving representations of the topology of triangular meshes can be classified into two major categories: lossless and lossy. Lossless methods usually refine meshes progressively with vertex-adding techniques [2, 3]. Such approaches can reconstruct the original mesh perfectly from a simple initial mesh, but they do not provide good parametrizations relating surface levels. Lossy methods apply regular (quaternary) surface subdivision schemes to base meshes to approximate irregular meshes [1, 4]. Although not able to recover the original topology (connectivity) exactly, the regular subdivision schemes enable us to construct 2D wavelets on triangular meshes so that geometry and color information of meshes can be expressed hierarchically and efficiently. To combine the advantages of these two different approaches, we are developing a new topology representation for arbitrary triangular meshes. Our method expresses the topology of meshes...