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In this paper, we describe a triangular lattice structuring method for 3D polygonal mesh data and a shape-adaptive wavelet transform of the structured geometry and textural data. Efficient representations of a 3D object data has attracted wide attention for transmission and storage of computer graphics data and interactive design in manufacturing. Polygonal mesh data, which consist of connectivity information, geometry data and textural data, are often used for representing a 3D object in many applications. We propose a method for structuring the polygonal mesh data on a triangular lattice plane with expanded nodes. And a shape-adaptive wavelet coding method is applied to the structured geometry data considering the expanded nodes. Experimental results show that the proposed method gives better coding performance than the topologically assisted geometry compression scheme.