In this paper we present a new method of data hiding in 3D objects. This method is based on a 3D model represented by a cloud of vertices and a list of edges corresponding to the triangular mesh of the surface. The main idea of this method is to find and to synchronize particular areas that can be used to embed the message. The data hiding relies on the modification of the topology of edges in chosen areas. These modifications, as a consequence, have to change the structure of triangles constructed in these areas. This method has the advantage of not changing the position of the vertices of the 3D model. This invariant on the vertex positions allows us to carry out an embedding that is robust to the affine transformations of type rotation, translation or zoom.