diff --git a/BGL/test/BGL/graph_concept_Linear_cell_complex.cpp b/BGL/test/BGL/graph_concept_Linear_cell_complex.cpp
index c2a002739c6..165e099dd7f 100644
--- a/BGL/test/BGL/graph_concept_Linear_cell_complex.cpp
+++ b/BGL/test/BGL/graph_concept_Linear_cell_complex.cpp
@@ -8,20 +8,7 @@
 
 typedef CGAL::Simple_cartesian<double> Kernel;
 typedef CGAL::Linear_cell_complex_traits<3, Kernel> MyTraits;
-
-struct Myitem
-{
-  template<class Refs>
-  struct Dart_wrapper
-  {
-    typedef CGAL::Tag_true Darts_with_id;
-    typedef CGAL::Cell_attribute_with_point_and_id< Refs > Vertex_attribute;
-    typedef CGAL::Cell_attribute_with_id< Refs > Face_attribute;
-    typedef CGAL::cpp11::tuple<Vertex_attribute, void, Face_attribute> Attributes;
-  };
-};
-
-typedef CGAL::Linear_cell_complex_for_combinatorial_map<2, 3, MyTraits, Myitem> LCC;
+typedef CGAL::Linear_cell_complex_for_bgl_combinatorial_map<2, 3, MyTraits> LCC;
 
 typedef boost::graph_traits< LCC > Traits;
 typedef Traits::edge_descriptor edge_descriptor;
diff --git a/BGL/test/BGL/test_Prefix.h b/BGL/test/BGL/test_Prefix.h
index c16a3ecbca9..7599c7080fc 100644
--- a/BGL/test/BGL/test_Prefix.h
+++ b/BGL/test/BGL/test_Prefix.h
@@ -15,9 +15,7 @@
 
 #include <CGAL/boost/graph/graph_traits_Polyhedron_3.h>
 
-#include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
-#include <CGAL/Linear_cell_complex_incremental_builder_v2.h>
-#include <CGAL/Linear_cell_complex_constructors.h>
+#include <CGAL/Linear_cell_complex_for_bgl_combinatorial_map.h>
 #include <CGAL/boost/graph/graph_traits_Linear_cell_complex.h>
 #include <CGAL/boost/graph/properties_Linear_cell_complex.h>
 
@@ -40,20 +38,7 @@ typedef Kernel::Triangle_3 Triangle_3;
 typedef Kernel::Iso_cuboid_3 Iso_cuboid_3;
 
 typedef CGAL::Linear_cell_complex_traits<3, Kernel> MyTraits;
-
-struct Myitem
-{
-  template<class Refs>
-  struct Dart_wrapper
-  {
-    typedef CGAL::Tag_true Darts_with_id;
-    typedef CGAL::Cell_attribute_with_point_and_id< Refs > Vertex_attribute;
-    typedef CGAL::Cell_attribute_with_id< Refs > Face_attribute;
-    typedef CGAL::cpp11::tuple<Vertex_attribute, void, Face_attribute> Attributes;
-  };
-};
-
-typedef CGAL::Linear_cell_complex_for_combinatorial_map<2, 3, MyTraits, Myitem> LCC;
+typedef CGAL::Linear_cell_complex_for_bgl_combinatorial_map<2, 3, MyTraits> LCC;
 
 
 #ifdef CGAL_USE_SURFACE_MESH
@@ -147,7 +132,7 @@ bool read_a_mesh(LCC& lcc, const std::string& str) {
   bool success = in.good();
   if(success)
   {
-    CGAL::load_off_v2(lcc, in);
+    CGAL::load_off_for_bgl(lcc, in);
     assert(lcc.is_valid());
   }
   return success;
diff --git a/Combinatorial_map/include/CGAL/Dart.h b/Combinatorial_map/include/CGAL/Dart.h
index 4098cca4c16..557cd2c7c83 100644
--- a/Combinatorial_map/include/CGAL/Dart.h
+++ b/Combinatorial_map/include/CGAL/Dart.h
@@ -23,6 +23,7 @@
 #include <CGAL/assertions.h>
 #include <CGAL/tuple.h>
 #include <bitset>
+#include <CGAL/Cell_attribute.h>
 
 namespace CGAL {
 
diff --git a/Convex_hull_3/examples/Convex_hull_3/dynamic_hull_LCC_3.cpp b/Convex_hull_3/examples/Convex_hull_3/dynamic_hull_LCC_3.cpp
index c5dfe5aceba..885f78830c3 100644
--- a/Convex_hull_3/examples/Convex_hull_3/dynamic_hull_LCC_3.cpp
+++ b/Convex_hull_3/examples/Convex_hull_3/dynamic_hull_LCC_3.cpp
@@ -3,28 +3,16 @@
 #include <CGAL/Delaunay_triangulation_3.h>
 #include <CGAL/algorithm.h>
 #include <CGAL/convex_hull_3_to_face_graph.h>
-#include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
 #include <CGAL/boost/graph/graph_traits_Linear_cell_complex.h>
+#include <CGAL/boost/graph/properties_Linear_cell_complex.h>
 #include <list>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel     K;
 typedef K::Point_3                                              Point_3;
 typedef CGAL::Delaunay_triangulation_3<K>                       Delaunay;
 typedef Delaunay::Vertex_handle                                 Vertex_handle;
-
-typedef CGAL::Linear_cell_complex_traits<3, K> MyTraits;
-struct Myitem
-{
-  template<class Refs>
-  struct Dart_wrapper
-  {
-    typedef CGAL::Tag_true Darts_with_id;
-    typedef CGAL::Cell_attribute_with_point_and_id< Refs > Vertex_attribute;
-    typedef CGAL::Cell_attribute_with_id< Refs > Face_attribute;
-    typedef CGAL::cpp11::tuple<Vertex_attribute, void, Face_attribute> Attributes;
-  };
-};
-typedef CGAL::Linear_cell_complex_for_combinatorial_map<2, 3, MyTraits, Myitem> LCC;
+typedef CGAL::Linear_cell_complex_traits<3, K>                  MyTraits;
+typedef CGAL::Linear_cell_complex_for_bgl_combinatorial_map<2, 3, MyTraits> LCC;
 
 int main()
 {
diff --git a/Linear_cell_complex/include/CGAL/Linear_cell_complex_for_bgl_combinatorial_map.h b/Linear_cell_complex/include/CGAL/Linear_cell_complex_for_bgl_combinatorial_map.h
new file mode 100644
index 00000000000..78dd0f712c0
--- /dev/null
+++ b/Linear_cell_complex/include/CGAL/Linear_cell_complex_for_bgl_combinatorial_map.h
@@ -0,0 +1,162 @@
+// Copyright (c) 2017 CNRS and LIRIS' Establishments (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public License as
+// published by the Free Software Foundation; either version 3 of the License,
+// or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+//
+// Author(s)     : Guillaume Damiand <guillaume.damiand@liris.cnrs.fr>
+//
+#ifndef CGAL_LINEAR_CELL_COMPLEX_FOR_BGL_COMBINATORIAL_MAP_H
+#define CGAL_LINEAR_CELL_COMPLEX_FOR_BGL_COMBINATORIAL_MAP_H 1
+
+#include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
+#include <CGAL/Linear_cell_complex_traits.h>
+#include <CGAL/CMap_linear_cell_complex_storages.h>
+#include <CGAL/Cell_attribute_with_point.h>
+
+namespace CGAL {
+
+  /** @file Linear_cell_complex_for_bgl_combinatorial_map.h
+   * Definition of a linear cell complex based on combinatorial map, to use with BGL.
+   * This cmap has points associated to all vertices and faces enables. Moreover
+   * these cells have id.
+   */
+
+  struct Linear_cell_complex_bgl_min_items
+  {
+    /// Dart_wrapper defines the type of darts used.
+    template <class LCC>
+    struct Dart_wrapper
+    {
+      typedef CGAL::Tag_true Darts_with_id;
+      typedef CGAL::Cell_attribute_with_point_and_id<LCC> Vertex_attribute;
+      typedef CGAL::Cell_attribute_with_id<LCC> Face_attribute;
+      typedef CGAL::cpp11::tuple<Vertex_attribute, void, Face_attribute> Attributes;
+    };
+  };
+  
+  // Linear_cell_complex_for_bgl_combinatorial_map class.
+  template < unsigned int d_, unsigned int ambient_dim = d_,
+             class Traits_ = Linear_cell_complex_traits<ambient_dim>,
+             class Items_ = Linear_cell_complex_bgl_min_items,
+             class Alloc_ = CGAL_ALLOCATOR(int),
+             template<unsigned int,class,class,class,class>
+             class CMap = Combinatorial_map_base,
+             class Storage_ = CMap_linear_cell_complex_storage_1<d_, ambient_dim,
+                                                                 Traits_, Items_,
+                                                                 Alloc_> >
+    class Linear_cell_complex_for_bgl_combinatorial_map:
+        public Linear_cell_complex_for_combinatorial_map
+                                       <d_, ambient_dim, Traits_,
+                                        Items_, Alloc_, CMap, Storage_>
+    {
+    public:
+      typedef Linear_cell_complex_for_bgl_combinatorial_map<d_, ambient_dim,
+                          Traits_, Items_, Alloc_, CMap, Storage_>  Self;
+
+      typedef Linear_cell_complex_for_combinatorial_map<d_, ambient_dim,
+                          Traits_, Items_, Alloc_, CMap, Storage_> Base;
+
+      typedef Traits_ Traits;
+      typedef Items_  Items;
+      typedef Alloc_  Alloc;
+
+      static const unsigned int ambient_dimension = Base::ambient_dimension;
+      static const unsigned int dimension = Base::dimension;
+
+      typedef typename Base::Dart_handle       Dart_handle;
+      typedef typename Base::Dart_const_handle Dart_const_handle;
+      typedef typename Base::Helper            Helper;
+
+      typedef typename Base::Point  Point;
+      typedef typename Base::Vector Vector;
+      typedef typename Base::FT     FT;
+
+      typedef typename Base::Dart_range Dart_range;
+
+      typedef typename Base::template Attribute_type<0>::type Vertex_attribute;
+      typedef typename Base::template Attribute_handle<0>::type
+      Vertex_attribute_handle;
+      typedef typename Base::template Attribute_const_handle<0>::type
+      Vertex_attribute_const_handle;
+
+      typedef typename Base::template Attribute_range<0>::type
+      Vertex_attribute_range;
+      typedef typename Base::template Attribute_const_range<0>::type
+      Vertex_attribute_const_range;
+
+      typedef typename Base::template Attribute_type<2>::type Face_attribute;
+      typedef typename Base::template Attribute_handle<2>::type
+      Face_attribute_handle;
+      typedef typename Base::template Attribute_const_handle<2>::type
+      Face_attribute_const_handle;
+
+      typedef typename Base::template Attribute_range<2>::type
+      Face_attribute_range;
+      typedef typename Base::template Attribute_const_range<2>::type
+      Face_attribute_const_range;
+
+      typedef typename Base::size_type size_type;
+
+      typedef typename Base::Use_index Use_index;
+      typedef typename Base::Storage Storage;
+      typedef typename Base::Exception_no_more_available_mark
+      Exception_no_more_available_mark;
+
+      Linear_cell_complex_for_bgl_combinatorial_map() : Base()
+      {}
+
+      /** Copy the given linear cell complex into *this.
+       *  Note that both LCC can have different dimensions and/or non void attributes.
+       *  @param alcc the linear cell complex to copy.
+       *  @post *this is valid.
+       */
+      Linear_cell_complex_for_bgl_combinatorial_map(const Self& alcc) : Base(alcc)
+      {}
+
+      template < class LCC2 >
+      Linear_cell_complex_for_bgl_combinatorial_map(const LCC2& alcc) : Base(alcc)
+      {}      
+
+      template < class LCC2, typename Converters >
+      Linear_cell_complex_for_bgl_combinatorial_map(const LCC2& alcc,
+                                                    Converters& converters) :
+        Base(alcc, converters)
+      {}
+
+      template < class LCC2, typename Converters, typename DartInfoConverter >
+      Linear_cell_complex_for_bgl_combinatorial_map(const LCC2& alcc,
+                                                    Converters& converters,
+                                                    const DartInfoConverter&
+                                                    dartinfoconverter) :
+        Base(alcc, converters, dartinfoconverter)
+      {}
+
+      template < class LCC2, typename Converters, typename DartInfoConverter,
+                 typename PointConverter >
+      Linear_cell_complex_for_bgl_combinatorial_map(const LCC2& alcc,
+                                                    Converters& converters,
+                                                    const DartInfoConverter&
+                                                    dartinfoconverter,
+                                                    const PointConverter&
+                                                    pointconverter) :
+        Base(alcc, converters, dartinfoconverter, pointconverter)
+      {}
+
+    };
+
+} // namespace CGAL
+
+#endif // CGAL_LINEAR_CELL_COMPLEX_FOR_BGL_COMBINATORIAL_MAP_H //
+// EOF //
diff --git a/Linear_cell_complex/include/CGAL/Linear_cell_complex_incremental_builder_v2.h b/Linear_cell_complex/include/CGAL/Linear_cell_complex_incremental_builder_for_bgl.h
similarity index 89%
rename from Linear_cell_complex/include/CGAL/Linear_cell_complex_incremental_builder_v2.h
rename to Linear_cell_complex/include/CGAL/Linear_cell_complex_incremental_builder_for_bgl.h
index b74523a476b..eeabd190e7f 100644
--- a/Linear_cell_complex/include/CGAL/Linear_cell_complex_incremental_builder_v2.h
+++ b/Linear_cell_complex/include/CGAL/Linear_cell_complex_incremental_builder_for_bgl.h
@@ -1,4 +1,4 @@
-// Copyright (c) 2011 CNRS and LIRIS' Establishments (France).
+// Copyright (c) 2017 CNRS and LIRIS' Establishments (France).
 // All rights reserved.
 //
 // This file is part of CGAL (www.cgal.org); you can redistribute it and/or
@@ -17,10 +17,10 @@
 //
 // Author(s)     : Guillaume Damiand <guillaume.damiand@liris.cnrs.fr>
 //
-#ifndef CGAL_LINEAR_CELL_COMPLEX_INCREMENTAL_BUILDER_V2_H
-#define CGAL_LINEAR_CELL_COMPLEX_INCREMENTAL_BUILDER_V2_H 1
+#ifndef CGAL_LINEAR_CELL_COMPLEX_INCREMENTAL_BUILDER_FOR_BGL_H
+#define CGAL_LINEAR_CELL_COMPLEX_INCREMENTAL_BUILDER_FOR_BGL_H 1
 
-#include <CGAL/Linear_cell_complex.h>
+#include <CGAL/Linear_cell_complex_constructors.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/IO/File_header_OFF.h>
 #include <CGAL/IO/File_scanner_OFF.h>
@@ -35,7 +35,7 @@ namespace CGAL {
  * associated with faces, non existing dart having no 2-attribute associated.
  */
   template < class LCC_ >
-  class Linear_cell_complex_incremental_builder_3_v2
+  class Linear_cell_complex_incremental_builder_for_bgl
   {
   public:
     typedef LCC_ LCC;
@@ -44,11 +44,11 @@ namespace CGAL {
     typedef typename LCC::Point                   Point_3;
     typedef typename LCC::size_type               size_type;
 
-    Linear_cell_complex_incremental_builder_3_v2(LCC & alcc) :
+    Linear_cell_complex_incremental_builder_for_bgl(LCC & alcc) :
       lcc(alcc)
     {}
 
-    Vertex_attribute_handle add_vertex (const Point_3& p)
+    Vertex_attribute_handle add_vertex(const Point_3& p)
     {
       Vertex_attribute_handle res = lcc.create_vertex_attribute(p);
       vertex_map.push_back(res);
@@ -162,8 +162,6 @@ namespace CGAL {
           assert(lcc.template is_free<0>(lcc.template beta<2>(other)));
           lcc.basic_link_beta_1(it, lcc.template beta<2>(other));
 
-          // For BGL halfedge graph, darts of border vertices must be border darts.
-// NOT NEEDED ??          lcc.template set_dart_of_attribute<0>(lcc.vertex_attribute(it), it);
           ++nb;
         }
       }
@@ -218,15 +216,15 @@ namespace CGAL {
     typename LCC::template Attribute_handle<2>::type face_attrib;
   };
 
-  template < class LCC >
-  void load_off_v2(LCC& alcc, std::istream& in)
+  template<class LCC>
+  void load_off_for_bgl(LCC& alcc, std::istream& in)
   {
     File_header_OFF  m_file_header;
     File_scanner_OFF scanner( in, m_file_header.verbose());
     if ( ! in) return;
     m_file_header = scanner;  // Remember file header after return.
 
-    Linear_cell_complex_incremental_builder_3_v2<LCC> B( alcc);
+    Linear_cell_complex_incremental_builder_for_bgl<LCC> B( alcc);
     B.begin_surface( scanner.size_of_vertices(),
                      scanner.size_of_facets(),
                      scanner.size_of_halfedges());
@@ -299,14 +297,29 @@ namespace CGAL {
   }
 
   template<class LCC>
-  void load_off_v2(LCC& alcc, const char* filename)
+  void load_off_for_bgl(LCC& alcc, const char* filename)
   {
     std::ifstream input(filename);
     if (input.is_open())
-      load_off_v2(alcc, input);
+      load_off_for_bgl(alcc, input);
   }
+  
+  template < class LCC >
+  void write_off_for_bgl(LCC& alcc, std::ostream& out)
+  {
+    // TODO (pehraps add a selector in the generic write_off function ?
+    write_off(alcc, out);
+  }
+  
+  template < class LCC >
+  void write_off_for_bgl(LCC& alcc, const char* filename)
+  {
+    // TODO (pehraps add a selector in the generic write_off function ?
+    write_off(alcc, filename);
+  }
+  
 
 } //namespace CGAL
 
-#endif // CGAL_LINEAR_CELL_COMPLEX_INCREMENTAL_BUILDER_V2_H //
+#endif // CGAL_LINEAR_CELL_COMPLEX_INCREMENTAL_BUILDER_FOR_BGL_H //
 // EOF //
diff --git a/Linear_cell_complex/include/CGAL/boost/graph/graph_traits_Linear_cell_complex.h b/Linear_cell_complex/include/CGAL/boost/graph/graph_traits_Linear_cell_complex.h
index 36106f0d5f9..246da592f8a 100644
--- a/Linear_cell_complex/include/CGAL/boost/graph/graph_traits_Linear_cell_complex.h
+++ b/Linear_cell_complex/include/CGAL/boost/graph/graph_traits_Linear_cell_complex.h
@@ -31,28 +31,30 @@
 #include <CGAL/boost/graph/properties_Linear_cell_complex.h>
 #include <CGAL/boost/graph/graph_traits_HalfedgeDS.h>
 
-#include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
+#include <CGAL/Linear_cell_complex_for_bgl_combinatorial_map.h>
+#include <CGAL/Linear_cell_complex_incremental_builder_for_bgl.h>
 #include <CGAL/Dart_iterators.h>
+
 #include <CGAL/boost/graph/helpers.h>
 #include <CGAL/iterator.h>
 
-#define CGAL_LCC_TEMPLATE_ARGS template < unsigned int d_, unsigned int ambient_dim, \
-                                          class Traits_,                \
-                                          class Items_,                 \
-                                          class Alloc_,                 \
-                                          template<unsigned int, class,class,class,class> \
-                                          class LCC,                   \
-                                          class Storage_>
-#define CGAL_LCC_TEMPLATE_ARGS_NOTEND template < unsigned int d_, unsigned int ambient_dim, \
-                                          class Traits_,                \
-                                          class Items_,                 \
-                                          class Alloc_,                 \
-                                          template<unsigned int, class,class,class,class> \
-                                          class LCC,                   \
-                                          class Storage_,
+#define CGAL_LCC_TEMPLATE_ARGS template<unsigned int d_, unsigned int ambient_dim, \
+                                        class Traits_,                \
+                                        class Items_,                 \
+                                        class Alloc_,                 \
+                                        template<unsigned int,class,class,class,class> \
+                                        class CMap,                   \
+                                        class Storage_>
+#define CGAL_LCC_TEMPLATE_ARGS_NOTEND template<unsigned int d_, unsigned int ambient_dim, \
+                                        class Traits_,                \
+                                        class Items_,                 \
+                                        class Alloc_,                 \
+                                        template<unsigned int,class,class,class,class> \
+                                        class CMap,                   \
+                                        class Storage_,
 
-#define CGAL_LCC_TYPE CGAL::Linear_cell_complex_for_combinatorial_map \
-                <d_, ambient_dim, Traits_, Items_, Alloc_, LCC, Storage_>
+#define CGAL_LCC_TYPE CGAL::Linear_cell_complex_for_bgl_combinatorial_map \
+                <d_, ambient_dim, Traits_, Items_, Alloc_, CMap, Storage_>
 
 namespace CGAL {
 
diff --git a/Linear_cell_complex/include/CGAL/boost/graph/properties_Linear_cell_complex.h b/Linear_cell_complex/include/CGAL/boost/graph/properties_Linear_cell_complex.h
index 6d36b6d6c52..61d85c770d1 100644
--- a/Linear_cell_complex/include/CGAL/boost/graph/properties_Linear_cell_complex.h
+++ b/Linear_cell_complex/include/CGAL/boost/graph/properties_Linear_cell_complex.h
@@ -21,7 +21,7 @@
 #define CGAL_BOOST_GRAPH_PROPERTIES_LINEAR_CELL_COMPLEX_H
 
 #include <CGAL/boost/graph/properties.h>
-#include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
+#include <CGAL/Linear_cell_complex_for_bgl_combinatorial_map.h>
 #include <CGAL/Unique_hash_map.h>
 #include <CGAL/boost/graph/properties_Polyhedron_3.h>
 
@@ -29,7 +29,7 @@
              class Traits_, \
              class Items_, \
              class Alloc_, \
-             template<unsigned int, class, class, class, class> \
+             template<unsigned int,class,class,class,class> \
              class CMap, \
              class Storage_
 
@@ -40,7 +40,7 @@
              CMap, \
              Storage_
 
-#define CGAL_LCC_TYPE CGAL::Linear_cell_complex_for_combinatorial_map\
+#define CGAL_LCC_TYPE CGAL::Linear_cell_complex_for_bgl_combinatorial_map\
            <d_, ambient_dim, Traits_, Items_, Alloc_, CMap , Storage_>
 
 namespace CGAL {
diff --git a/Polygon_mesh_processing/examples/Polygon_mesh_processing/corefinement_LCC.cpp b/Polygon_mesh_processing/examples/Polygon_mesh_processing/corefinement_LCC.cpp
index e34b4e0ad71..447ae597dff 100644
--- a/Polygon_mesh_processing/examples/Polygon_mesh_processing/corefinement_LCC.cpp
+++ b/Polygon_mesh_processing/examples/Polygon_mesh_processing/corefinement_LCC.cpp
@@ -1,8 +1,5 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
-#include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
 #include <CGAL/boost/graph/graph_traits_Linear_cell_complex.h>
-#include <CGAL/Linear_cell_complex_incremental_builder_v2.h>
-#include <CGAL/Linear_cell_complex_constructors.h>
 
 #include <CGAL/Polygon_mesh_processing/corefinement.h>
 
@@ -10,20 +7,8 @@
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
 typedef Kernel::Point_3 Point;
-
 typedef CGAL::Linear_cell_complex_traits<3, Kernel> MyTraits;
-struct Myitem
-{
-  template<class Refs>
-  struct Dart_wrapper
-  {
-    typedef CGAL::Tag_true Darts_with_id;
-    typedef CGAL::Cell_attribute_with_point_and_id< Refs > Vertex_attribute;
-    typedef CGAL::Cell_attribute_with_id< Refs > Face_attribute;
-    typedef CGAL::cpp11::tuple<Vertex_attribute, void, Face_attribute> Attributes;
-  };
-};
-typedef CGAL::Linear_cell_complex_for_combinatorial_map<2, 3, MyTraits, Myitem> LCC;
+typedef CGAL::Linear_cell_complex_for_bgl_combinatorial_map<2, 3, MyTraits> LCC;
 
 namespace PMP = CGAL::Polygon_mesh_processing;
 
@@ -34,8 +19,8 @@ int main(int argc, char* argv[])
   std::ifstream input(filename1);
 
   LCC mesh1, mesh2;
-  CGAL::load_off_v2(mesh1, filename1);
-  CGAL::load_off_v2(mesh2, filename2);
+  CGAL::load_off_for_bgl(mesh1, filename1);
+  CGAL::load_off_for_bgl(mesh2, filename2);
 
   std::cout << "Number of vertices before corefinement "
             << num_vertices(mesh1) << " and "
@@ -48,10 +33,10 @@ int main(int argc, char* argv[])
             << num_vertices(mesh2) << "\n";
 
   std::ofstream output("mesh1_refined.off");
-  CGAL::write_off(mesh1, output);
+  CGAL::write_off_for_bgl(mesh1, output);
   output.close();
   output.open("mesh2_refined.off");
-  CGAL::write_off(mesh2, output);  
+  CGAL::write_off_for_bgl(mesh2, output);  
   output.close();
 
   return 0;
diff --git a/Polygon_mesh_processing/examples/Polygon_mesh_processing/hole_filling_example_LCC.cpp b/Polygon_mesh_processing/examples/Polygon_mesh_processing/hole_filling_example_LCC.cpp
index 4f9a2a3f1a0..a0d2a5d880c 100644
--- a/Polygon_mesh_processing/examples/Polygon_mesh_processing/hole_filling_example_LCC.cpp
+++ b/Polygon_mesh_processing/examples/Polygon_mesh_processing/hole_filling_example_LCC.cpp
@@ -1,7 +1,5 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
-#include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
 #include <CGAL/boost/graph/graph_traits_Linear_cell_complex.h>
-#include <CGAL/Linear_cell_complex_incremental_builder_v2.h>
 #include <CGAL/Linear_cell_complex_constructors.h>
 
 #include <CGAL/Polygon_mesh_processing/triangulate_hole.h>
@@ -13,20 +11,8 @@
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
 typedef Kernel::Point_3 Point;
-
 typedef CGAL::Linear_cell_complex_traits<3, Kernel> MyTraits;
-struct Myitem
-{
-  template<class Refs>
-  struct Dart_wrapper
-  {
-    typedef CGAL::Tag_true Darts_with_id;
-    typedef CGAL::Cell_attribute_with_point_and_id< Refs > Vertex_attribute;
-    typedef CGAL::Cell_attribute_with_id< Refs > Face_attribute;
-    typedef CGAL::cpp11::tuple<Vertex_attribute, void, Face_attribute> Attributes;
-  };
-};
-typedef CGAL::Linear_cell_complex_for_combinatorial_map<2, 3, MyTraits, Myitem> LCC;
+typedef CGAL::Linear_cell_complex_for_bgl_combinatorial_map<2, 3, MyTraits> LCC;
 
 typedef boost::graph_traits<LCC>::halfedge_descriptor halfedge_descriptor;
 typedef boost::graph_traits<LCC>::face_descriptor     face_descriptor;
@@ -37,7 +23,7 @@ int main(int argc, char* argv[])
 {
   const char* filename = (argc > 1) ? argv[1] : "data/mech-holes-shark.off";
   LCC mesh;
-  CGAL::load_off_v2(mesh, filename);
+  CGAL::load_off_for_bgl(mesh, filename);
 
   // Incrementally fill the holes
   unsigned int nb_holes = 0;
@@ -70,7 +56,7 @@ int main(int argc, char* argv[])
   
   std::ofstream out("filled_LCC.off");
   out.precision(17);
-  CGAL::write_off(mesh, out);
+  CGAL::write_off_for_bgl(mesh, out);
 
   return 0;
 }
diff --git a/Ridges_3/examples/Ridges_3/Ridges_Umbilics_LCC.cpp b/Ridges_3/examples/Ridges_3/Ridges_Umbilics_LCC.cpp
index 707d379e580..f3e726b2d14 100644
--- a/Ridges_3/examples/Ridges_3/Ridges_Umbilics_LCC.cpp
+++ b/Ridges_3/examples/Ridges_3/Ridges_Umbilics_LCC.cpp
@@ -1,8 +1,6 @@
 #include <CGAL/Simple_cartesian.h>
 #include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
 #include <CGAL/boost/graph/graph_traits_Linear_cell_complex.h>
-#include <CGAL/Linear_cell_complex_incremental_builder_v2.h>
-#include <CGAL/Linear_cell_complex_constructors.h>
 
 #include "PolyhedralSurf_rings.h"
 #include "compute_normals.h"
@@ -22,20 +20,8 @@ typedef CGAL::Simple_cartesian<double>  Kernel;
 typedef Kernel::FT                      FT;
 typedef Kernel::Point_3                 Point_3;
 typedef Kernel::Vector_3                Vector_3;
-
 typedef CGAL::Linear_cell_complex_traits<3, Kernel> MyTraits;
-struct Myitem
-{
-  template<class Refs>
-  struct Dart_wrapper
-  {
-    typedef CGAL::Tag_true Darts_with_id;
-    typedef CGAL::Cell_attribute_with_point_and_id< Refs > Vertex_attribute;
-    typedef CGAL::Cell_attribute_with_id< Refs > Face_attribute;
-    typedef CGAL::cpp11::tuple<Vertex_attribute, void, Face_attribute> Attributes;
-  };
-};
-typedef CGAL::Linear_cell_complex_for_combinatorial_map<2, 3, MyTraits, Myitem> LCC;
+typedef CGAL::Linear_cell_complex_for_bgl_combinatorial_map<2, 3, MyTraits> LCC;
 
 typedef LCC PolyhedralSurf;
 
@@ -299,7 +285,7 @@ int main()
 
   //load the model from <mesh.off>
   PolyhedralSurf P;
-  CGAL::load_off_v2(P, if_name.c_str());
+  CGAL::load_off_for_bgl(P, if_name.c_str());
   fprintf(stderr, "loadMesh %d Ves %d Facets\n",
 	  (int)num_vertices(P), (int)num_faces(P));
   if(verbose)
diff --git a/Surface_mesh_segmentation/examples/Surface_mesh_segmentation/segmentation_from_sdf_values_LCC_example.cpp b/Surface_mesh_segmentation/examples/Surface_mesh_segmentation/segmentation_from_sdf_values_LCC_example.cpp
index dc74b39d2d3..2ceee58985f 100644
--- a/Surface_mesh_segmentation/examples/Surface_mesh_segmentation/segmentation_from_sdf_values_LCC_example.cpp
+++ b/Surface_mesh_segmentation/examples/Surface_mesh_segmentation/segmentation_from_sdf_values_LCC_example.cpp
@@ -1,6 +1,5 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
-#include <CGAL/Linear_cell_complex_incremental_builder_v2.h>
 #include <CGAL/boost/graph/graph_traits_Linear_cell_complex.h>
 #include <CGAL/mesh_segmentation.h>
 
@@ -12,27 +11,14 @@
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
 typedef CGAL::Linear_cell_complex_traits<3, Kernel> MyTraits;
-
-struct Myitem
-{
-  template<class Refs>
-  struct Dart_wrapper
-  {
-    typedef CGAL::Tag_true Darts_with_id;
-    typedef CGAL::Cell_attribute_with_point_and_id< Refs > Vertex_attribute;
-    typedef CGAL::Cell_attribute_with_id< Refs > Face_attribute;
-    typedef CGAL::cpp11::tuple<Vertex_attribute, void, Face_attribute> Attributes;
-  };
-};
-
-typedef CGAL::Linear_cell_complex_for_combinatorial_map<2, 3, MyTraits, Myitem> LCC;
+typedef CGAL::Linear_cell_complex_for_bgl_combinatorial_map<2, 3, MyTraits> LCC;
 typedef typename LCC::Attribute_const_handle<2>::type Facet_const_handle;
 
 int main()
 {
     // create and read LCC
     LCC mesh;
-    CGAL::load_off_v2(mesh, "data/cactus.off");
+    CGAL::load_off_for_bgl(mesh, "data/cactus.off");
 
     // create a property-map for SDF values
     typedef CGAL::Unique_hash_map<Facet_const_handle, double> Facet_double_map;
diff --git a/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_linear_cell_complex.cpp b/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_linear_cell_complex.cpp
index 91cc3d076c9..9f9398d8d8c 100644
--- a/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_linear_cell_complex.cpp
+++ b/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_linear_cell_complex.cpp
@@ -1,8 +1,5 @@
 #include <iostream>
 #include <fstream>
-#include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
-#include <CGAL/Linear_cell_complex_constructors.h>
-#include <CGAL/Linear_cell_complex_incremental_builder_v2.h>
 #include <CGAL/boost/graph/graph_traits_Linear_cell_complex.h>
 // Simplification function
 #include <CGAL/Surface_mesh_simplification/edge_collapse.h>
@@ -13,20 +10,7 @@
 
 typedef CGAL::Simple_cartesian<double> Kernel;
 typedef CGAL::Linear_cell_complex_traits<3, Kernel> MyTraits;
-
-struct Myitem
-{
-  template<class Refs>
-  struct Dart_wrapper
-  {
-    typedef CGAL::Tag_true Darts_with_id;
-    typedef CGAL::Cell_attribute_with_point_and_id< Refs > Vertex_attribute;
-    typedef CGAL::Cell_attribute_with_id< Refs > Face_attribute;
-    typedef CGAL::cpp11::tuple<Vertex_attribute, void, Face_attribute> Attributes;
-  };
-};
-
-typedef CGAL::Linear_cell_complex_for_combinatorial_map<2, 3, MyTraits, Myitem> LCC;
+typedef CGAL::Linear_cell_complex_for_bgl_combinatorial_map<2, 3, MyTraits> LCC;
 namespace SMS = CGAL::Surface_mesh_simplification ;
 
 int main( int argc, char** argv )
@@ -39,7 +23,7 @@ int main( int argc, char** argv )
 
   LCC lcc;
   std::ifstream is(argv[1]);
-  CGAL::load_off_v2(lcc, is);
+  CGAL::load_off_for_bgl(lcc, is);
 
   lcc.display_characteristics(std::cout)<<", is_valid="<<CGAL::is_valid(lcc)<<std::endl;
 
@@ -65,8 +49,7 @@ int main( int argc, char** argv )
 
   lcc.display_characteristics(std::cout)<<", is_valid="<<CGAL::is_valid(lcc)<<std::endl;
 
-  std::ofstream os(argc > 2 ? argv[2] : "out.off");
-  CGAL::write_off(lcc, os);
+  CGAL::write_off_for_bgl(lcc, (argc > 2 ? argv[2] : "out.off"));
   return EXIT_SUCCESS;
 }
 // EOF //
diff --git a/Surface_mesh_skeletonization/examples/Surface_mesh_skeletonization/MCF_Skeleton_LCC_example.cpp b/Surface_mesh_skeletonization/examples/Surface_mesh_skeletonization/MCF_Skeleton_LCC_example.cpp
index 070d52102e6..f5de6ab41ea 100644
--- a/Surface_mesh_skeletonization/examples/Surface_mesh_skeletonization/MCF_Skeleton_LCC_example.cpp
+++ b/Surface_mesh_skeletonization/examples/Surface_mesh_skeletonization/MCF_Skeleton_LCC_example.cpp
@@ -1,5 +1,4 @@
 #include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
-#include <CGAL/Linear_cell_complex_incremental_builder_v2.h>
 #include <CGAL/boost/graph/graph_traits_Linear_cell_complex.h>
 #include <CGAL/Simple_cartesian.h>
 #include <CGAL/Mean_curvature_flow_skeletonization.h>
@@ -8,22 +7,8 @@
 
 typedef CGAL::Simple_cartesian<double>                        Kernel;
 typedef Kernel::Point_3                                       Point;
-
-typedef CGAL::Linear_cell_complex_traits<3, Kernel> MyTraits;
-
-struct Myitem
-{
-  template<class Refs>
-  struct Dart_wrapper
-  {
-    typedef CGAL::Tag_true Darts_with_id;
-    typedef CGAL::Cell_attribute_with_point_and_id< Refs > Vertex_attribute;
-    typedef CGAL::Cell_attribute_with_id< Refs > Face_attribute;
-    typedef CGAL::cpp11::tuple<Vertex_attribute, void, Face_attribute> Attributes;
-  };
-};
-
-typedef CGAL::Linear_cell_complex_for_combinatorial_map<2, 3, MyTraits, Myitem> LCC;
+typedef CGAL::Linear_cell_complex_traits<3, Kernel>           MyTraits;
+typedef CGAL::Linear_cell_complex_for_bgl_combinatorial_map<2, 3, MyTraits> LCC;
 typedef boost::graph_traits<LCC>::vertex_descriptor    vertex_descriptor;
 
 typedef CGAL::Mean_curvature_flow_skeletonization<LCC> Skeletonization;
@@ -36,7 +21,7 @@ typedef Skeleton::edge_descriptor                             Skeleton_edge;
 int main(int argc, char* argv[])
 {
   LCC lcc;
-  CGAL::load_off_v2(lcc, "data/elephant.off");
+  CGAL::load_off_for_bgl(lcc, "data/elephant.off");
 
   Skeleton skeleton;
   Skeletonization mcs(lcc);
diff --git a/Surface_mesh_skeletonization/examples/Surface_mesh_skeletonization/simple_mcfskel_LCC_example.cpp b/Surface_mesh_skeletonization/examples/Surface_mesh_skeletonization/simple_mcfskel_LCC_example.cpp
index fd5be7360d6..099991e4f79 100644
--- a/Surface_mesh_skeletonization/examples/Surface_mesh_skeletonization/simple_mcfskel_LCC_example.cpp
+++ b/Surface_mesh_skeletonization/examples/Surface_mesh_skeletonization/simple_mcfskel_LCC_example.cpp
@@ -1,6 +1,4 @@
 #include <CGAL/Simple_cartesian.h>
-#include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
-#include <CGAL/Linear_cell_complex_incremental_builder_v2.h>
 #include <CGAL/boost/graph/graph_traits_Linear_cell_complex.h>
 #include <CGAL/boost/graph/properties_Linear_cell_complex.h>
 #include <CGAL/extract_mean_curvature_flow_skeleton.h>
@@ -11,21 +9,8 @@
 
 typedef CGAL::Simple_cartesian<double>                        Kernel;
 typedef Kernel::Point_3                                       Point;
-typedef CGAL::Linear_cell_complex_traits<3, Kernel> MyTraits;
-
-struct Myitem
-{
-  template<class Refs>
-  struct Dart_wrapper
-  {
-    typedef CGAL::Tag_true Darts_with_id;
-    typedef CGAL::Cell_attribute_with_point_and_id< Refs > Vertex_attribute;
-    typedef CGAL::Cell_attribute_with_id< Refs > Face_attribute;
-    typedef CGAL::cpp11::tuple<Vertex_attribute, void, Face_attribute> Attributes;
-  };
-};
-
-typedef CGAL::Linear_cell_complex_for_combinatorial_map<2, 3, MyTraits, Myitem> LCC;
+typedef CGAL::Linear_cell_complex_traits<3, Kernel>           MyTraits;
+typedef CGAL::Linear_cell_complex_for_bgl_combinatorial_map<2, 3, MyTraits> LCC;
 
 typedef boost::graph_traits<LCC>::vertex_descriptor    vertex_descriptor;
 
@@ -65,7 +50,7 @@ struct Display_polylines{
 int main(int argc, char* argv[])
 {
   LCC lcc;
-  CGAL::load_off_v2(lcc, "data/elephant.off");
+  CGAL::load_off_for_bgl(lcc, "data/elephant.off");
 
   Skeleton skeleton;