Polygonal meshes are used in various fields ranging from CAD to gaming and web based applications. Reducing the size required for storing and transmitting these meshes by taking advantage of redundancies is an important aspect in all of these cases. In this paper, we present a connectivity based compression approach that predicts attributes and stores differences to the predictions together with minimal connectivity information. It is an extension to the Cut-Border Machine and applicable to arbitrary manifold and non-manifold polygonal meshes containing multiple attributes of different types. It compresses both the connectivity and attributes without loss outside of re-ordering vertices and polygons. In addition, an optional quantization step can be used to further reduce the data if a certain loss of accuracy is acceptable. Our method outperforms state-of-the-art compression techniques, including specialized triangle mesh compression approaches when applicable. Typical compression rates for our approach range from 2:1 to 6:1 for lossless compression and up to 25:1 when quantizing to 14 bit accuracy.