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The efficient progressive transmission of a textured 3D model, which has a texture image mapped on a geometric mesh, requires careful organization of the bit stream to quickly present high-resolution visualization on the user's screen. Bit rates for the mesh and the texture need to be properly balanced so that the decoded model has the best visual fidelity during transmission. This problem is addressed in the paper, and a bit allocation framework is proposed. In particular, the relative importance of the mesh geometry and the texture image on visual fidelity is estimated using a fast quality measure (FQM). Optimal bit distribution between the mesh and the texture is then computed under the criterion of maximizing the quality measured by FQM. Both the quality measure and the bit allocation algorithm are designed with low computation complexity. Empirical studies show that not only the bit allocation framework maximizes the receiving quality of the textured 3D model, but also it does not require sending additional information to indicate bit boundaries between the mesh and the texture in the multiplexed bit stream, which makes the streaming application more robust to bit errors that may occur randomly during transmission.