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, using at least one processor, 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, wherein the quantization of geometric information causes gaps in some of the cluster meshes, and wherein the local quantization unit performs a scaling of a grid of the local coordinate system to suit the cluster mesh having the largest size among the generated cluster meshes, and applies the local coordinate system adopting the same scaling to other cluster meshes to reduce the gaps caused by quantization of the geometric information.