In this paper, we address the challenging problem of the 3D point cloud compression required to ensure efficient transmission and storage. We introduce a new hierarchical geometry representation based on adaptive Tree-Structured Point-Lattice Vector Quantization (TSPLVQ). This representation enables hierarchically structured 3D content that improves the compression performance for static point cloud. The novelty of the proposed scheme lies in adaptive selection of the optimal quantization scheme of the geometric information, that better leverage the intrinsic correlations in point cloud. Based on its adaptive and multiscale structure, two quantization schemes are dedicated to project recursively the 3D point clouds into a series of embedded truncated cubic lattices. At each step of the process, the optimal quantization scheme is selected according to a rate-distortion cost in order to achieve the best trade-off between coding rate and geometry distortion, such that the compression flexibility and performance can be greatly improved. Experimental results show the interest of the proposed multi-scale method for lossy compression of geometry.