diff --git a/Combinatorial_map/include/CGAL/Cell_attribute.h b/Combinatorial_map/include/CGAL/Cell_attribute.h
index 269b40cc72b..0186fa44ac0 100644
--- a/Combinatorial_map/include/CGAL/Cell_attribute.h
+++ b/Combinatorial_map/include/CGAL/Cell_attribute.h
@@ -89,6 +89,12 @@ namespace CGAL {
     template<typename CMap, unsigned int i, typename T>
     friend struct internal::Decrease_attribute_functor_run;
 
+    template <typename CMap, typename Attrib>
+    friend struct internal::Reverse_orientation_of_map_functor;
+
+    template <typename CMap, typename Attrib>
+    friend struct internal::Reverse_orientation_of_connected_component_functor;
+
   public:
     typedef Tag_false                            Supports_cell_dart;
 
@@ -195,6 +201,12 @@ namespace CGAL {
     template<typename CMap, unsigned int i, typename T>
     friend struct internal::Decrease_attribute_functor_run;
 
+    template <typename CMap, typename Attrib>
+    friend struct internal::Reverse_orientation_of_map_functor;
+
+    template <typename CMap, typename Attrib>
+    friend struct internal::Reverse_orientation_of_connected_component_functor;
+
   public:
     typedef Tag_true                             Supports_cell_dart;
 
diff --git a/Combinatorial_map/include/CGAL/Combinatorial_map.h b/Combinatorial_map/include/CGAL/Combinatorial_map.h
index 6b221f600c4..862435422a0 100644
--- a/Combinatorial_map/include/CGAL/Combinatorial_map.h
+++ b/Combinatorial_map/include/CGAL/Combinatorial_map.h
@@ -2200,6 +2200,27 @@ namespace CGAL {
       if ( update_attributes ) unsew<i>(adart);
       else topo_unsew<i>(adart);
     }
+      
+    /** Reverse the orientation (swap beta 0 & 1 links) of the entire map.
+     * A valid map after this operation remains valid.
+     * @param none
+     * @return none
+     */
+    void reverse_orientation()
+    {
+      internal::Reverse_orientation_of_map_functor<Self>::run(this);
+    }
+    
+    /** Reverse the orientation (swap beta 0 & 1 links) of the connected
+     * component containing the given dart.
+     * A valid map after this operation remains valid.
+     * @param adart handle to a dart
+     * @return none
+     */
+    void reverse_orientation_connected_component (Dart_handle adart)
+    {
+      internal::Reverse_orientation_of_connected_component_functor<Self>::run(this, adart);
+    }
 
     /** Count the marked cells (at least one marked dart).
      * @param amark the mark to consider.
diff --git a/Combinatorial_map/include/CGAL/Dart.h b/Combinatorial_map/include/CGAL/Dart.h
index 0af7239ea26..8269c222f78 100644
--- a/Combinatorial_map/include/CGAL/Dart.h
+++ b/Combinatorial_map/include/CGAL/Dart.h
@@ -72,6 +72,12 @@ namespace CGAL {
 
     template <typename Map,unsigned int i>
     friend struct internal::link_beta_functor;
+      
+    template <typename CMap, typename Attrib>
+    friend struct internal::Reverse_orientation_of_map_functor;
+
+    template <typename CMap, typename Attrib>
+    friend struct internal::Reverse_orientation_of_connected_component_functor;
 
   public:
     typedef Dart<d,Refs>                     Self;
@@ -272,6 +278,16 @@ namespace CGAL {
       Helper::template Foreach_enabled_attributes<Init_attribute_functor>::
         run(this);
     }
+    
+    /** Copy constructor:
+     * @param adart a dart.
+     */
+    Dart(const std::bitset<NB_MARKS>& /*amarks*/, const Dart& adart) : mmarks(adart.mmarks),
+    mattribute_handles(adart.mattribute_handles)
+    {
+      for (unsigned int i = 0; i <= dimension; ++i)
+        mbeta[i] = adart.mbeta[i];
+    }
 
     /** Return the mark value of a given mark number.
      * @param amark the mark number.
diff --git a/Combinatorial_map/include/CGAL/internal/Combinatorial_map_internal_functors.h b/Combinatorial_map/include/CGAL/internal/Combinatorial_map_internal_functors.h
index 1bd03d8f345..83e576f0556 100644
--- a/Combinatorial_map/include/CGAL/internal/Combinatorial_map_internal_functors.h
+++ b/Combinatorial_map/include/CGAL/internal/Combinatorial_map_internal_functors.h
@@ -630,6 +630,198 @@ struct Test_is_same_attribute_functor
 template<typename Map1, typename Map2>
 bool Test_is_same_attribute_functor<Map1, Map2>::value = true;
 // ****************************************************************************
+/// Functor to reverse the orientation of a combinatorial map
+template <typename CMap, typename Attrib =
+          typename CMap::Helper::template Attribute_type<0>::type>
+struct Reverse_orientation_of_map_functor
+{
+  static void run(CMap *amap)
+  {
+    int mark = amap->get_new_mark();
+    CGAL_precondition(amap->is_whole_map_unmarked(mark));
+    CGAL_precondition(amap->is_valid());
+    for (typename CMap::Dart_range::iterator current_dart=amap->darts().begin(),
+           last_dart = amap->darts().end(); current_dart!=last_dart;
+         ++current_dart)
+    {
+      if (amap->is_marked(current_dart, mark)) continue;
+      typename CMap::Dart_handle first_dart_in_cell= current_dart;
+      typename CMap::Dart_handle current_dart_in_cell=
+        first_dart_in_cell->beta(1);
+      typename CMap::Helper::template Attribute_handle<0>::type
+        attribute_for_first_dart=current_dart_in_cell->template attribute<0>();
+      attribute_for_first_dart->inc_nb_refs();
+      do {
+        amap->mark(current_dart_in_cell, mark);
+        typename CMap::Dart_handle previous_dart_in_cell=
+          current_dart_in_cell->beta(0);
+        typename CMap::Dart_handle next_dart_in_cell=
+          current_dart_in_cell->beta(1);
+        typename CMap::Helper::template Attribute_handle<0>::type
+          next_attribute=next_dart_in_cell->template attribute<0>();
+        // One line error???
+        CGAL::internal::Set_i_attribute_of_dart_functor<CMap, 0>::
+          run(amap, current_dart_in_cell, next_attribute);
+        current_dart_in_cell->basic_link_beta(previous_dart_in_cell, 1);
+        current_dart_in_cell->basic_link_beta(next_dart_in_cell, 0);
+        current_dart_in_cell = current_dart_in_cell->beta(0);
+      }
+      while (current_dart_in_cell != first_dart_in_cell);
+      amap->mark(current_dart_in_cell, mark);
+      typename CMap::Dart_handle previous_dart_in_cell=
+        current_dart_in_cell->beta(0);
+      typename CMap::Dart_handle next_dart_in_cell=
+        current_dart_in_cell->beta(1);
+      CGAL::internal::Set_i_attribute_of_dart_functor<CMap, 0>::
+        run(amap, current_dart_in_cell, attribute_for_first_dart);
+              attribute_for_first_dart->dec_nb_refs();
+      current_dart_in_cell->basic_link_beta(previous_dart_in_cell, 1);
+      current_dart_in_cell->basic_link_beta(next_dart_in_cell, 0);
+    }
+    amap->negate_mark(mark);
+    CGAL_postcondition(amap->is_whole_map_unmarked(mark));
+    CGAL_postcondition(amap->is_valid());
+    amap->free_mark(mark);
+  }
+};
+// ****************************************************************************
+// Specialization for void 0-attributes
+template <typename CMap>
+struct Reverse_orientation_of_map_functor<CMap, CGAL::Void>
+{
+  static void run(CMap *amap)
+  {
+    int mark = amap->get_new_mark();
+    CGAL_precondition(amap->is_whole_map_unmarked(mark));
+    CGAL_precondition(amap->is_valid());
+    for (typename CMap::Dart_range::iterator current_dart=amap->darts().begin(),
+         last_dart = amap->darts().end(); current_dart!=last_dart;
+         ++current_dart)
+    {
+      if (amap->is_marked(current_dart, mark)) continue;
+      for (typename CMap::template Dart_of_cell_range<2>::iterator
+             current_dart_in_cell=amap->template darts_of_cell<2>(current_dart).
+             begin(), last_dart_in_cell=amap->template darts_of_cell<2>
+             (current_dart).end(); current_dart_in_cell!=last_dart_in_cell;
+           ++current_dart_in_cell)
+      {
+        amap->mark(current_dart_in_cell, mark);
+        typename CMap::Dart_handle previous_dart_in_cell=
+          current_dart_in_cell->beta(0);
+        typename CMap::Dart_handle next_dart_in_cell=
+          current_dart_in_cell->beta(1);
+        current_dart_in_cell->basic_link_beta(previous_dart_in_cell, 1);
+        current_dart_in_cell->basic_link_beta(next_dart_in_cell, 0);
+      }
+    }
+    amap->negate_mark(mark);
+    CGAL_postcondition(amap->is_whole_map_unmarked(mark));
+    CGAL_postcondition(amap->is_valid());
+    amap->free_mark(mark);
+  }
+};
+// ****************************************************************************
+/// Functor to reverse the orientation of a connected component in a given map
+template <typename CMap, typename Attrib=
+          typename CMap::Helper::template Attribute_type<0>::type>
+struct Reverse_orientation_of_connected_component_functor
+{
+  static void run(CMap *amap, typename CMap::Dart_handle adart)
+  {
+    int mark = amap->get_new_mark();
+    CGAL_precondition(amap->is_whole_map_unmarked(mark));
+    for (typename CMap::template Dart_of_cell_range<CMap::dimension+1>::iterator
+           current_dart=amap->template darts_of_cell<CMap::dimension+1>(adart).
+           begin(), last_dart=amap->template darts_of_cell<CMap::dimension+1>
+           (adart).end(); current_dart!=last_dart; ++current_dart)
+    {
+      if (amap->is_marked(current_dart, mark)) continue;
+      typename CMap::Dart_handle first_dart_in_cell=current_dart;
+      typename CMap::Dart_handle current_dart_in_cell=
+        first_dart_in_cell->beta(1);
+      typename CMap::Helper::template Attribute_handle<0>::type
+        attribute_for_first_dart=current_dart_in_cell->template attribute<0>();
+      attribute_for_first_dart->inc_nb_refs();
+      do {
+        amap->mark(current_dart_in_cell, mark);
+        typename CMap::Dart_handle previous_dart_in_cell=
+          current_dart_in_cell->beta(0);
+        typename CMap::Dart_handle next_dart_in_cell=
+          current_dart_in_cell->beta(1);
+        typename CMap::Helper::template Attribute_handle<0>::type
+          next_attribute=next_dart_in_cell->template attribute<0>();
+
+        CGAL::internal::Set_i_attribute_of_dart_functor<CMap, 0>::
+          run(amap, current_dart_in_cell, next_attribute);
+        current_dart_in_cell->basic_link_beta(previous_dart_in_cell, 1);
+        current_dart_in_cell->basic_link_beta(next_dart_in_cell, 0);
+        current_dart_in_cell = current_dart_in_cell->beta(0);
+      }
+      while (current_dart_in_cell != first_dart_in_cell);
+      amap->mark(current_dart_in_cell, mark);
+      typename CMap::Dart_handle previous_dart_in_cell=
+        current_dart_in_cell->beta(0);
+      typename CMap::Dart_handle next_dart_in_cell=
+        current_dart_in_cell->beta(1);
+      CGAL::internal::Set_i_attribute_of_dart_functor<CMap, 0>::
+          run(amap, current_dart_in_cell, attribute_for_first_dart);
+      attribute_for_first_dart->dec_nb_refs();
+      current_dart_in_cell->basic_link_beta(previous_dart_in_cell, 1);
+      current_dart_in_cell->basic_link_beta(next_dart_in_cell, 0);
+    }
+    for (typename CMap::template Dart_of_cell_range<CMap::dimension+1>::iterator
+           current_dart=amap->template darts_of_cell<CMap::dimension+1>(adart).
+           begin(), last_dart=amap->template darts_of_cell<CMap::dimension+1>
+           (adart).end(); current_dart!=last_dart; ++current_dart)
+    {
+      amap->unmark(current_dart, mark);
+    }
+    CGAL_postcondition(amap->is_whole_map_unmarked(mark));
+    amap->free_mark(mark);
+  }
+};
+// ****************************************************************************
+// Specialization for void 0-attributes
+template <typename CMap>
+struct Reverse_orientation_of_connected_component_functor<CMap, CGAL::Void>
+{
+  static void run(CMap *amap, typename CMap::Dart_handle adart)
+  {
+    int mark = amap->get_new_mark();
+    CGAL_precondition(amap->is_whole_map_unmarked(mark));
+    for (typename CMap::template Dart_of_cell_range<CMap::dimension+1>::iterator
+           current_dart=amap->template darts_of_cell<CMap::dimension+1>(adart).
+           begin(), last_dart=amap->template darts_of_cell<CMap::dimension+1>
+           (adart).end(); current_dart!=last_dart; ++current_dart)
+    {
+      if (amap->is_marked(current_dart, mark)) continue;
+      for (typename CMap::template Dart_of_cell_range<2>::iterator
+             current_dart_in_cell=amap->template darts_of_cell<2>(current_dart).
+             begin(), last_dart_in_cell=amap->template darts_of_cell<2>
+             (current_dart).end(); current_dart_in_cell!=last_dart_in_cell;
+           ++current_dart_in_cell)
+      {
+        amap->mark(current_dart_in_cell, mark);
+        typename CMap::Dart_handle previous_dart_in_cell=
+          current_dart_in_cell->beta(0);
+        typename CMap::Dart_handle next_dart_in_cell=
+          current_dart_in_cell->beta(1);
+        current_dart_in_cell->basic_link_beta(previous_dart_in_cell, 1);
+        current_dart_in_cell->basic_link_beta(next_dart_in_cell, 0);
+      }
+    }
+    for (typename CMap::template Dart_of_cell_range<CMap::dimension+1>::iterator
+           current_dart=amap->template darts_of_cell<CMap::dimension+1>(adart).
+           begin(), last_dart=amap->template darts_of_cell<CMap::dimension+1>
+           (adart).end(); current_dart!=last_dart; ++current_dart)
+    {
+      amap->unmark(current_dart, mark);
+    }
+    CGAL_postcondition(amap->is_whole_map_unmarked(mark));
+    amap->free_mark(mark);
+  }
+};
+// ****************************************************************************
 // Beta functor, used to combine several beta.
 #ifndef CGAL_CFG_NO_CPP0X_VARIADIC_TEMPLATES
 template<typename Dart_handle, typename ... Betas>
diff --git a/Linear_cell_complex/test/Linear_cell_complex/Linear_cell_complex_4_test.h b/Linear_cell_complex/test/Linear_cell_complex/Linear_cell_complex_4_test.h
index d19dee3bc22..a21e31ea478 100644
--- a/Linear_cell_complex/test/Linear_cell_complex/Linear_cell_complex_4_test.h
+++ b/Linear_cell_complex/test/Linear_cell_complex/Linear_cell_complex_4_test.h
@@ -284,6 +284,12 @@ bool test_LCC_4()
     return false;
   }
 
+  lcc.reverse_orientation();
+  lcc.reverse_orientation();
+
+  lcc.reverse_orientation_connected_component(dh1);
+  lcc.reverse_orientation_connected_component(dh1);
+
   /*    import_from_polyhedron<LCC>(lcc,ap);
 
         lcc.clear();