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The transmission and storage of large amounts of vertex geometry data are required for rendering geometrically detailed 3D graphic models. To mitigate bandwidth requirements, vector quantization (VQ) is an effective lossy vertex data compression technique for triangular meshes. In this paper, we present a new vertex encoding scheme based on VQ. Particularly, we propose a novel prediction method that generalizes the conventional parallelogram prediction method and further reduces the prediction error. During the encoding process, the vertex to be encoded is predicted by all the encoded vertices neighboring to it within a large edge-distance, instead of the encoded vertices directly connecting to it with 1-edge-distance as in the conventional parallelogram prediction. Experimental results show that, compared with the vertex encoding scheme based on the conventional parallelogram prediction, the proposed algorithm consistently achieves a higher encoding quality at the same bit rate.