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In many applications surfaces with a large number of primitives occur. Geometry compression reduces storage space and transmission time for such models. A special case is given by polygonal isosurfaces generated from gridded volume data. However most current state-of-the-art geometry compression systems do not capitalize on the structure that is characteristic of such isosurfaces, namely that the surfaces are defined by a set of vertices on edges of the grid. In a previous paper we proposed a compression method for isosurfaces that exploits this feature. In this paper we use the same coding approach, however, including context models for the encoding of the symbol streams. We report improved compression ratios for complex isosurfaces from a CT scan of a human head Our coder outperformed state-of-the-art general purpose geometry compression methods. We also report results obtained by two predictive coding methods based on least squares function fitting and a surface relaxation algorithm.