3D meshes are widely used today in very different domains for examples; game, medical diagnostic, CAD (computed aided design) or more recently 3D printing. In this paper we provide a new data hiding method that has a huge capacity, c p=3×c×(n−1) bits where n is the vertex number of the mesh and c is a non null positive integer. Our proposed method synchronizes vertices along a Hamiltonian path, thus we obtained an ordered list of edges. To do this, we have developed a method based on the displacement of a 3D vertex relative to its father in the path. Its new location is computed with static arithmetic coding (SAC) in order to embed data on each coordinate of a vector defined by an edge. Thus, the proposed method is set as a function of the message in order to control the distortions. Moreover, it allows to set the capacity while achieving a better security. Experimental results show that the method has a high capacity and a low distortion while ensuring security of the hidden message.