diff --git a/Alpha_wrap_3/include/CGAL/Alpha_wrap_3/internal/Alpha_wrap_3.h b/Alpha_wrap_3/include/CGAL/Alpha_wrap_3/internal/Alpha_wrap_3.h
index 8d3d837034b..b886add0ff6 100644
--- a/Alpha_wrap_3/include/CGAL/Alpha_wrap_3/internal/Alpha_wrap_3.h
+++ b/Alpha_wrap_3/include/CGAL/Alpha_wrap_3/internal/Alpha_wrap_3.h
@@ -727,7 +727,7 @@ private:
     std::cout << "> Extract possibly non-manifold wrap... ()" << std::endl;
 #endif
 
-    clear(output_mesh);
+    remove_all_elements(output_mesh);
 
     CGAL_assertion_code(for(auto cit=m_tr.finite_cells_begin(), cend=m_tr.finite_cells_end(); cit!=cend; ++cit))
     CGAL_assertion(cit->tds_data().is_clear());
@@ -814,7 +814,7 @@ private:
     CGAL_assertion_code(for(Vertex_handle v : m_tr.finite_vertex_handles()))
     CGAL_assertion(!is_non_manifold(v));
 
-    clear(output_mesh);
+    remove_all_elements(output_mesh);
 
     std::vector<Point_3> points;
     std::vector<std::array<std::size_t, 3> > faces;
diff --git a/BGL/doc/BGL/PackageDescription.txt b/BGL/doc/BGL/PackageDescription.txt
index 89497261a96..883c1b3ad46 100644
--- a/BGL/doc/BGL/PackageDescription.txt
+++ b/BGL/doc/BGL/PackageDescription.txt
@@ -690,6 +690,7 @@ user might encounter.
 - `CGAL::make_grid()`
 
 - `CGAL::clear()`
+- `CGAL::remove_all_elements()`
 - `CGAL::copy_face_graph()`
 
 - `CGAL::set_triangulation_ids()`
diff --git a/BGL/include/CGAL/IO/polygon_mesh_io.h b/BGL/include/CGAL/IO/polygon_mesh_io.h
index b8b86d45f8f..21f61087ab6 100644
--- a/BGL/include/CGAL/IO/polygon_mesh_io.h
+++ b/BGL/include/CGAL/IO/polygon_mesh_io.h
@@ -45,25 +45,25 @@ bool read_polygon_mesh(std::istream& is,
   ok = read_OFF(is, g, np, false);
   if(ok)
     return true;
-  g.clear();
+  clear(g);
   is.clear();//reset the error state
   is.seekg (0, is.beg);
   ok = read_OBJ(is, g, np, false);
   if(ok)
     return true;
-  g.clear();
+  clear(g);
   is.clear();
   is.seekg (0, is.beg);
   ok = read_PLY(is, g, np, false);
   if(ok)
     return true;
-  g.clear();
+  clear(g);
   is.clear();
   is.seekg (0, is.beg);
   ok = read_STL(is, g, np, false);
   if(ok)
     return true;
-  g.clear();
+  clear(g);
   is.clear();
   is.seekg (0, is.beg);
   ok = read_GOCAD(is, g, np, false);
diff --git a/BGL/include/CGAL/boost/graph/IO/STL.h b/BGL/include/CGAL/boost/graph/IO/STL.h
index d2cb78c4524..9796b462917 100644
--- a/BGL/include/CGAL/boost/graph/IO/STL.h
+++ b/BGL/include/CGAL/boost/graph/IO/STL.h
@@ -172,7 +172,7 @@ bool read_STL(const std::string& fname,
     {
       return true;
     }
-    g.clear();
+    clear(g);
   }
   std::ifstream is(fname);
   CGAL::IO::set_mode(is, CGAL::IO::ASCII);
diff --git a/BGL/include/CGAL/boost/graph/IO/polygon_mesh_io.h b/BGL/include/CGAL/boost/graph/IO/polygon_mesh_io.h
index 84189cf7373..edb858a160f 100644
--- a/BGL/include/CGAL/boost/graph/IO/polygon_mesh_io.h
+++ b/BGL/include/CGAL/boost/graph/IO/polygon_mesh_io.h
@@ -11,6 +11,8 @@
 #ifndef CGAL_BOOST_GRAPH_POLYGON_MESH_IO_H
 #define CGAL_BOOST_GRAPH_POLYGON_MESH_IO_H
 
+
 #include <CGAL/IO/polygon_mesh_io.h>
 
+
 #endif // CGAL_BOOST_GRAPH_POLYGON_MESH_IO_H
diff --git a/BGL/include/CGAL/boost/graph/helpers.h b/BGL/include/CGAL/boost/graph/helpers.h
index 32b99ba397d..75673493e0d 100644
--- a/BGL/include/CGAL/boost/graph/helpers.h
+++ b/BGL/include/CGAL/boost/graph/helpers.h
@@ -837,25 +837,6 @@ bool is_hexahedron(typename boost::graph_traits<FaceGraph>::halfedge_descriptor
 
 namespace internal {
 
-template<typename FaceGraph>
-inline
-std::enable_if_t<Has_member_clear<FaceGraph>::value, void>
-clear_impl(FaceGraph& g)
-{ g.clear(); }
-
-template<typename FaceGraph>
-inline
-std::enable_if_t<!Has_member_clear<FaceGraph>::value, void>
-clear_impl(FaceGraph& g)
-{
-  while(std::begin(edges(g))!=std::end(edges(g)))
-    remove_edge(*std::begin(edges(g)), g);
-  while(std::begin(faces(g))!=std::end(faces(g)))
-    remove_face(*std::begin(faces(g)), g);
-  while(std::begin(vertices(g))!=std::end(vertices(g)))
-    remove_vertex(*std::begin(vertices(g)), g);
-}
-
 template <class FaceGraph>
 void swap_vertices(typename boost::graph_traits<FaceGraph>::vertex_descriptor& p,
                    typename boost::graph_traits<FaceGraph>::vertex_descriptor& q,
@@ -965,24 +946,86 @@ void collect_garbage(Graph&)
  * \ingroup PkgBGLHelperFct
  *
  * removes all vertices, faces and halfedges from a graph. Calls
- * `remove_edge()`, `remove_vertex()`, and `remove_face()` for each
- * edge, vertex or face.
+ * \link MutableHalfedgeGraph `remove_vertex()`\endlink,
+ * \link MutableHalfedgeGraph `remove_edge()`\endlink, and
+ * \link MutableFaceGraph `remove_face()`\endlink, for each vertex, edge, and face.
+ *
+ * Note that some graphs have a specialized version of this function to improve
+ * complexity.
+ *
+ * @warning This function does not perform anything more than what is advertised above. It is
+ * up to the user to e.g. clean garbage or remove internal property maps (if relevant, and desired).
+ *
+ * @tparam FaceGraph model of `MutableHalfedgeGraph` and `MutableFaceGraph`
+ *
+ * @param g the graph whose elements will be removed
+ *
+ * @sa `CGAL::clear()`
+ **/
+template<typename FaceGraph>
+void remove_all_elements(FaceGraph& g)
+{
+  while(std::begin(edges(g)) != std::end(edges(g)))
+    remove_edge(*std::begin(edges(g)), g);
+  while(std::begin(faces(g)) != std::end(faces(g)))
+    remove_face(*std::begin(faces(g)), g);
+  while(std::begin(vertices(g)) != std::end(vertices(g)))
+    remove_vertex(*std::begin(vertices(g)), g);
+
+  CGAL_postcondition(std::distance(std::cbegin(vertices(g)), std::cend(vertices(g))) == 0);
+  CGAL_postcondition(std::distance(std::cbegin(edges(g)), std::cend(edges(g))) == 0);
+  CGAL_postcondition(std::distance(std::cbegin(faces(g)), std::cend(faces(g))) == 0);
+}
+
+namespace internal {
+
+template<typename FaceGraph>
+inline
+std::enable_if_t<Has_member_clear<FaceGraph>::value, void>
+clear_impl(FaceGraph& g)
+{
+  g.clear();
+}
+
+template<typename FaceGraph>
+inline
+std::enable_if_t<!Has_member_clear<FaceGraph>::value, void>
+clear_impl(FaceGraph& g)
+{
+  remove_all_elements(g);
+}
+
+} // namespace internal
+
+/**
+ * \ingroup PkgBGLHelperFct
+ *
+ * removes all vertices, faces and halfedges from a graph. Calls
+ * \link MutableHalfedgeGraph `remove_vertex()`\endlink,
+ * \link MutableHalfedgeGraph `remove_edge()`\endlink, and
+ * \link MutableFaceGraph `remove_face()`\endlink, for each vertex, edge, and face.
  *
  * If the graph has a member function `clear()`, it will be called
  * instead.
  *
+ * @warning If it exists, the `clear()` function of a graph might do more than
+ * simply remove elements. For example, `CGAL::Surface_mesh::clear()` collects garbage
+ * and removes *all* property maps added by a call to `CGAL::Surface_mesh::add_property_map()` for all simplex types.
+ *
  * @tparam FaceGraph model of `MutableHalfedgeGraph` and `MutableFaceGraph`
  *
  * @param g the graph to clear
  *
+ * @sa `CGAL::remove_all_elements()`
  **/
 template<typename FaceGraph>
 void clear(FaceGraph& g)
 {
   internal::clear_impl(g);
-  CGAL_postcondition(std::distance(std::begin(edges(g)),std::end(edges(g))) == 0);
-  CGAL_postcondition(std::distance(std::begin(vertices(g)),std::end(vertices(g))) == 0);
-  CGAL_postcondition(std::distance(std::begin(faces(g)),std::end(faces(g))) == 0);
+
+  CGAL_postcondition(std::distance(std::cbegin(vertices(g)), std::cend(vertices(g))) == 0);
+  CGAL_postcondition(std::distance(std::cbegin(edges(g)), std::cend(edges(g))) == 0);
+  CGAL_postcondition(std::distance(std::cbegin(faces(g)), std::cend(faces(g))) == 0);
 }
 
 /**
diff --git a/BGL/test/BGL/test_Face_filtered_graph.cpp b/BGL/test/BGL/test_Face_filtered_graph.cpp
index 9917b7d06a5..d83de2bbdc6 100644
--- a/BGL/test/BGL/test_Face_filtered_graph.cpp
+++ b/BGL/test/BGL/test_Face_filtered_graph.cpp
@@ -513,7 +513,7 @@ void test_invalid_selections()
   assert(pinched_fg.is_selection_valid());
 
   // this creates a non-manifold vertex (multiple umbrellas)
-  clear(mesh);
+  CGAL::clear(mesh);
   read_a_mesh(mesh, "data/genus3.off");
   assert(is_valid_polygon_mesh(mesh));
 
diff --git a/BGL/test/BGL/test_bgl_read_write.cpp b/BGL/test/BGL/test_bgl_read_write.cpp
index 694c8a9933f..962a53ba541 100644
--- a/BGL/test/BGL/test_bgl_read_write.cpp
+++ b/BGL/test/BGL/test_bgl_read_write.cpp
@@ -122,7 +122,7 @@ void test_bgl_OFF(const std::string filename)
   assert(ok);
   assert(num_vertices(fg) != 0 && num_faces(fg) != 0);
   is.close();
-  fg.clear();
+  CGAL::clear(fg);
 
   is.open(filename, std::ios::binary);
   ok = CGAL::IO::read_OFF(is, fg);
@@ -286,7 +286,7 @@ void test_bgl_OFF(const std::string filename)
 
     for(auto f : faces(fg))
       assert(get(fcm2, f) != CGAL::IO::Color());
-    fg.clear();
+    CGAL::clear(fg);
     is.close();
 
     is.open("data/full.off");
@@ -478,7 +478,7 @@ void test_bgl_PLY(const std::string filename,
   assert(filename != CGAL::data_file_path("meshes/colored_tetra.ply") || (num_vertices(fg) == 4 && num_faces(fg) == 4));
    if(!binary)
    {
-     fg.clear();
+     CGAL::clear(fg);
      is.open(filename, std::ios::binary);
      bool ok = CGAL::IO::read_PLY(is, fg, CGAL::parameters::use_binary_mode(false));
      is.close();
@@ -711,7 +711,6 @@ void test_bgl_GOCAD(const char* filename)
   assert(num_vertices(fg) != 0 && num_faces(fg) != 0);
 
   is.seekg(0);
-  fg.clear();
   CGAL::clear(fg);
   std::pair<std::string, std::string> name_and_color;
   ok = CGAL::IO::read_GOCAD(is, name_and_color, fg);
diff --git a/Installation/CHANGES.md b/Installation/CHANGES.md
index c46826b1d5f..c6940c7ae72 100644
--- a/Installation/CHANGES.md
+++ b/Installation/CHANGES.md
@@ -105,6 +105,12 @@ Release date: October 2023
     only affects custom point types where not all points in the same position
     are equivalent.
 
+### [CGAL and the Boost Graph Library (BGL)](https://doc.cgal.org/6.0/Manual/packages.html#PkgBGL)
+
+- Added the function `remove_all_elements()`, which removes vertices, halfedges, and faces
+  without collecting garbage and without removing properties.
+
+
 [Release 5.6](https://github.com/CGAL/cgal/releases/tag/v5.6)
 -----------
 
diff --git a/Polygon_mesh_processing/examples/Polygon_mesh_processing/cc_compatible_orientations.cpp b/Polygon_mesh_processing/examples/Polygon_mesh_processing/cc_compatible_orientations.cpp
index 646e94e9468..2c1b55c183c 100644
--- a/Polygon_mesh_processing/examples/Polygon_mesh_processing/cc_compatible_orientations.cpp
+++ b/Polygon_mesh_processing/examples/Polygon_mesh_processing/cc_compatible_orientations.cpp
@@ -43,7 +43,7 @@ void create_mesh_with_cc_to_orient(Mesh& mesh)
   }
 
   // load the soup into the mesh;
-  mesh.clear();
+  CGAL::clear(mesh);
   PMP::polygon_soup_to_polygon_mesh(points, triangles, mesh);
 }
 
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/clip.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/clip.h
index 9cf0e4b43a5..5926bab0020 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/clip.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/clip.h
@@ -738,7 +738,7 @@ bool clip(TriangleMesh& tm,
     case ON_NEGATIVE_SIDE:
       return true; // nothing to clip, the full mesh is on the negative side
     case ON_POSITIVE_SIDE:
-      clear(tm); // clear the mesh that is fully on the positive side
+      remove_all_elements(tm); // clear the mesh that is fully on the positive side
       return true;
     default:
       break;
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/connected_components.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/connected_components.h
index bffa8e6dca1..bdca099e32c 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/connected_components.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/connected_components.h
@@ -423,7 +423,7 @@ std::size_t keep_largest_connected_components(PolygonMesh& pmesh,
 
   if(nb_components_to_keep == 0)
   {
-    CGAL::clear(pmesh);
+    remove_all_elements(pmesh);
     return num;
   }
 
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/corefinement.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/corefinement.h
index c955aa8bdc3..105a74f51b9 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/corefinement.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/corefinement.h
@@ -266,11 +266,11 @@ corefine_and_compute_boolean_operations(
 
     if (output[Corefinement::TM1_MINUS_TM2] != std::nullopt)
       if (&tm1 == *output[Corefinement::TM1_MINUS_TM2])
-        clear(tm1);
+        remove_all_elements(tm1);
 
     if (output[Corefinement::TM2_MINUS_TM1] != std::nullopt)
       if (&tm1 == *output[Corefinement::TM2_MINUS_TM1])
-        clear(tm1);
+        remove_all_elements(tm1);
 
     return CGAL::make_array(true, true, true, true);
   }
@@ -282,7 +282,7 @@ corefine_and_compute_boolean_operations(
     {
       for (int i=0; i<4; ++i)
         if (output[i] != std::nullopt)
-          clear(*(*output[i]));
+          remove_all_elements(*(*output[i]));
       return CGAL::make_array(true, true, true, true);
     }
     // tm2 is not empty
@@ -293,9 +293,9 @@ corefine_and_compute_boolean_operations(
                         parameters::vertex_point_map(vpm2),
                         parameters::vertex_point_map(*std::get<Corefinement::UNION>(vpm_out_tuple)));
     if (output[Corefinement::INTERSECTION] != std::nullopt)
-      clear(*(*output[Corefinement::INTERSECTION]));
+      remove_all_elements(*(*output[Corefinement::INTERSECTION]));
     if (output[Corefinement::TM1_MINUS_TM2] != std::nullopt)
-      clear(*(*output[Corefinement::TM1_MINUS_TM2]));
+      remove_all_elements(*(*output[Corefinement::TM1_MINUS_TM2]));
     if (output[Corefinement::TM2_MINUS_TM1] != std::nullopt)
       if (&tm2 != *output[Corefinement::TM2_MINUS_TM1])
         copy_face_graph(tm2,
@@ -315,9 +315,9 @@ corefine_and_compute_boolean_operations(
                           parameters::vertex_point_map(vpm1),
                           parameters::vertex_point_map(*std::get<Corefinement::UNION>(vpm_out_tuple)));
       if (output[Corefinement::INTERSECTION] != std::nullopt)
-        clear(*(*output[Corefinement::INTERSECTION]));
+        remove_all_elements(*(*output[Corefinement::INTERSECTION]));
       if (output[Corefinement::TM2_MINUS_TM1] != std::nullopt)
-        clear(*(*output[Corefinement::TM2_MINUS_TM1]));
+        remove_all_elements(*(*output[Corefinement::TM2_MINUS_TM1]));
       if (output[Corefinement::TM1_MINUS_TM2] != std::nullopt)
         if (&tm1 != *output[Corefinement::TM1_MINUS_TM2])
           copy_face_graph(tm1,
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/remesh_planar_patches.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/remesh_planar_patches.h
index 33514d6f2de..69ef710f616 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/remesh_planar_patches.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/remesh_planar_patches.h
@@ -1263,8 +1263,7 @@ bool decimate_meshes_with_common_interfaces_impl(TriangleMeshRange& meshes,
     }
     CGAL_assertion(is_polygon_soup_a_polygon_mesh(all_faces[mesh_id]));
 
-    //clear(tm);
-    tm.clear_without_removing_property_maps();
+    remove_all_elements(tm);
     polygon_soup_to_polygon_mesh(all_corners[mesh_id], all_faces[mesh_id],
                                  tm, parameters::default_values(), parameters::vertex_point_map(vpms[mesh_id]));
   }
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair_degeneracies.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair_degeneracies.h
index 1dde0a5b20d..19adcd48319 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair_degeneracies.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair_degeneracies.h
@@ -1934,7 +1934,7 @@ bool remove_degenerate_faces(const FaceRange& face_range,
 
   if(degenerate_face_set.size() == faces_size)
   {
-    clear(tmesh);
+    remove_all_elements(tmesh);
     return true;
   }
 
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/data_degeneracies/all_degen.off b/Polygon_mesh_processing/test/Polygon_mesh_processing/data_degeneracies/all_degen.off
new file mode 100644
index 00000000000..f579551770c
--- /dev/null
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/data_degeneracies/all_degen.off
@@ -0,0 +1,16 @@
+OFF
+7 7 0
+0 0 0
+1 1 0
+1 1 0
+2 2 0
+1 1 0
+2 2 0
+0.5 1 0
+3 0 2 1
+3 0 3 2
+3 4 3 5
+3 1 4 5
+3 1 2 6
+3 6 2 4
+3 6 4 1
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_repair_degeneracies.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_repair_degeneracies.cpp
index 847e9dbf615..dfbeee6f1ba 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_repair_degeneracies.cpp
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/test_pmp_repair_degeneracies.cpp
@@ -287,6 +287,11 @@ void test()
                                0, 1, // expected number of degenerate edges/faces in the selection
                                0, 0); // expected number of degenerate edges/faces in the mesh after partial removal
 
+  remove_degeneracies<K, Mesh>("data_degeneracies/all_degen.off",
+                               std::initializer_list<std::size_t>({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}), // edge selection
+                               std::initializer_list<std::size_t>({0, 1, 2, 3, 4, 5, 6}), // face selection
+                               4, 7, 4, 7, 0, 0);
+
   remove_degeneracies<K, Mesh>("data_degeneracies/degtri_four.off",
                                std::initializer_list<std::size_t>({1}),
                                std::initializer_list<std::size_t>({3}),
diff --git a/Polyhedron/include/CGAL/boost/graph/graph_traits_Polyhedron_3.h b/Polyhedron/include/CGAL/boost/graph/graph_traits_Polyhedron_3.h
index f8e6e9a21ca..7626c554fe1 100644
--- a/Polyhedron/include/CGAL/boost/graph/graph_traits_Polyhedron_3.h
+++ b/Polyhedron/include/CGAL/boost/graph/graph_traits_Polyhedron_3.h
@@ -313,6 +313,12 @@ set_halfedge(typename boost::graph_traits< CGAL::Polyhedron_3<Gt,I,HDS,A> >::ver
   static_cast<Sneak&>(*v).set_halfedge(h);
 }
 
+template<class Gt, class I, CGAL_HDS_PARAM_, class A>
+void
+remove_all_elements(CGAL::Polyhedron_3<Gt,I,HDS,A>& g)
+{
+  g.clear();
+}
 
 //
 // HalfedgeGraph
diff --git a/Surface_mesh/include/CGAL/boost/graph/graph_traits_Surface_mesh.h b/Surface_mesh/include/CGAL/boost/graph/graph_traits_Surface_mesh.h
index b46df17715b..29699dc1ddc 100644
--- a/Surface_mesh/include/CGAL/boost/graph/graph_traits_Surface_mesh.h
+++ b/Surface_mesh/include/CGAL/boost/graph/graph_traits_Surface_mesh.h
@@ -472,7 +472,6 @@ remove_vertex(typename boost::graph_traits<CGAL::Surface_mesh<P> >::vertex_descr
   sm.remove_vertex(v);
 }
 
-
 template <typename P>
 void
 remove_edge(typename boost::graph_traits<CGAL::Surface_mesh<P> >::vertex_descriptor u,
@@ -491,7 +490,6 @@ remove_edge(typename boost::graph_traits<CGAL::Surface_mesh<P> >::edge_descripto
   sm.remove_edge(e);
 }
 
-
 template <typename P>
 void
 remove_edge(typename boost::graph_traits<CGAL::Surface_mesh<P> >::edge_iterator eiter,
@@ -508,6 +506,13 @@ remove_face(typename boost::graph_traits<CGAL::Surface_mesh<P> >::face_descripto
   sm.remove_face(f);
 }
 
+template<typename P>
+void
+remove_all_elements(CGAL::Surface_mesh<P>& sm)
+{
+  sm.clear_without_removing_property_maps();
+}
+
 template<typename P>
 typename boost::graph_traits<CGAL::Surface_mesh<P> >::face_descriptor
 add_face(CGAL::Surface_mesh<P>& sm)