  Nef_polyhedron_2<T,Items,Mark> join(const Nef_polyhedron_2<T,Items,Mark>& N1) const
  /*{\Mop returns |\Mvar| $\cup$ |N1|. }*/
  { Nef_polyhedron_2<T,Items,Mark> res(pm(),false); // empty, no frame
    Overlayer D(res.pm());
    D.subdivide(pm(),N1.pm());
    OR _or; D.select(_or);
    res.clear_outer_face_cycle_marks();
    D.simplify(Except_frame_box_edges(res.pm()));
    return res;
  }
  Nef_polyhedron_2<T,Items,Mark> join(const Nef_polyhedron_2<T,Items,Mark>& N1) const
   
  { Nef_polyhedron_2<T,Items,Mark> res(pm(),false);  
    Overlayer D(res.pm());
    D.subdivide(pm(),N1.pm());
    OR _or; D.select(_or);
    res.clear_outer_face_cycle_marks();
    D.simplify(Except_frame_box_edges(res.pm()));
    return res;
  }