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In this paper, we propose a new geometry coding scheme for 3D objects. The prediction error of each vertex position along a vertex spanning tree is obtained in the Cartesian coordinate system (x,y,z), and transformed into the spherical coordinate system (r,θ,φ). The magnitude r of the prediction error is quantized by an optimal uniform quantizer, and the corresponding pair of (θ,φ) is encoded according to the magnitude of the quantized value of the radius. We partition the sphere of the radius r into n2 regions to allocate n2 quantization points over the sphere. Experimental results of the proposed method demonstrate improved coding efficiency.