This paper deals with the current trends of technologies which aim at representing efficiently 3D point cloud, they have become a popular challenge for processing, storing and conveying the data independently of how it was captured. Compressing attributes of 3D point clouds such as geometry, colours or normal directions remain challenging problem, since these signals are unstructured. We propose an adaptive Tree-Structured Point-Lattice Vector Quantization (TSPLVQ), resulting in hierarchically structured 3D content, to improve compression performance for static point cloud.The novelty of the proposed approach lies in adaptively selecting the optimal quantization scheme for the point cloud geometric data, such that its intrinsic correlations can be better exploited.Two quantization modes 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 mode is chosen according to a rate-distortion criterion 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. To achieve rate-distortion optimization, the core of the proposed method relies on an accurate estimation of the distortion inside each cubic voronoï, between fitting plane and cloud points, taking into account the visual rendering of the 3D object. We experimentally evaluated the interest of the proposed method for geometry compression and visualization tasks.