1. A system for compressing and decoding mesh data in a three-dimensional mesh model, comprising: a mesh data acquisition unit to acquire mesh data from a three-dimensional mesh model; a cluster mesh generation unit to generate a plurality of cluster meshes by using the mesh data; and a local quantization unit to quantize geometry information of respective vertexes through application of respective local coordinate systems to the respective cluster meshes and to generate quantized data of the respective vertexes included in the respective cluster meshes.