3D meshes are widely used today in very different domains for example; game, medical diagnostic, CAD (computed aided design) or more recently 3-D printing. In this paper, we provide a new data hiding method that has a huge capacity, cp = 3c(n - 1), where n is the vertex number of the mesh and c is an integer. The proposed method consists to compute a Hamiltonian path along the mesh as synchronization. At each step of path building, 3c bits are embedded. The embedding is designed to be a distance relation between a vertex and its father in the path. Moreover, the method uses static arithmetic coding to embed message information. We analyzed the proposed method by inserting RGB images in 3D meshes.