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Summary form only given. We address geometry coding of 3D models. Conventional geometry coding schemes quantize vertex positions using a bounding box before coding it by an entropy coder. However, in the proposed scheme, we first predict vertex positions and then quantize them differentially. Our geometry encoder consists of four stages: preprocessing, prediction, quantization, and entropy coding. Using a joint prediction, the encoder predicts vertex positions in a layer traversal order. Although the joint prediction is based on the parallelogram prediction, we use every possible preceding triangle to approximate the predicted vertex.