In many applications surfaces containing 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. We propose a compression method for isosurfaces that is designed to exploit this feature. We tested our method for several isosurfaces from a CT scan of a human head. For this data set our coder outperformed state-of-the-art geometry compression methods by a factor of 2.2 to 2.8 in terms of compression ratio.