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Many algorithms have been proposed for the task of efficient compression of triangular meshes. Geometric properties of the input data are usually exploited to obtain an accurate prediction of the data at the decoder. Considerations on how to improve the prediction usually focus on its normal part, assuming that the tangential part behaves similarly. In this paper, we show that knowledge of vertex valences might allow the decoder to form a prediction that is more accurate in the tangential direction, using a weighted parallelogram prediction. This idea can be easily implemented into existing compression algorithms, such as Edgebreaker, and it can be applied at different levels of sophistication, from very simple ones, that are computationally very cheap, to some more complex ones that provide an even better compression efficiency.