diff --git a/BGL/include/CGAL/boost/graph/graph_traits_Linear_cell_complex.h b/BGL/include/CGAL/boost/graph/graph_traits_Linear_cell_complex.h
index e6bf6211b8f..352d8b7ee4e 100644
--- a/BGL/include/CGAL/boost/graph/graph_traits_Linear_cell_complex.h
+++ b/BGL/include/CGAL/boost/graph/graph_traits_Linear_cell_complex.h
@@ -83,7 +83,7 @@ struct EdgeHandle : Dart_handle
   { return this->beta(2); }
   
   bool operator==(const EdgeHandle& h)
-  { return (*this)==h  /* TODO || h->beta(2)==*this */ ; }
+  { return (*this)==h  || h->get_f(2)==*this; }
 };
 
 template <class CMap, typename Dart_Iterator>
@@ -167,7 +167,7 @@ public :
   typedef typename CMap::size_type edges_size_type;
   typedef typename CMap::size_type faces_size_type;
   
-  typedef CGAL::In_edge_iterator<CMap> in_edge_iterator;
+  typedef CGAL::In_edge_iterator<CMap>  in_edge_iterator;
   typedef CGAL::Out_edge_iterator<CMap> out_edge_iterator;
 
   // nulls
@@ -424,8 +424,8 @@ halfedge(typename boost::graph_traits<CGAL_LCC_TYPE>::edge_descriptor e,
 CGAL_LCC_TEMPLATE_ARGS
 typename boost::graph_traits<CGAL_LCC_TYPE>::halfedge_descriptor
 halfedge(typename boost::graph_traits<CGAL_LCC_TYPE>::vertex_descriptor v,
-         const CGAL_LCC_TYPE&)
-{ return v->dart(); }
+         const CGAL_LCC_TYPE& cmap)
+{ return const_cast<CGAL_LCC_TYPE&>(cmap).template beta<2>(v->dart()); }
 
 CGAL_LCC_TEMPLATE_ARGS
 std::pair<
@@ -553,7 +553,6 @@ void set_halfedge(typename boost::graph_traits<CGAL_LCC_TYPE>::vertex_descriptor
                   CGAL_LCC_TYPE& cm)
 {
   //cm.template set_dart_of_attribute<0>(v, h);
-
   cm.template set_dart_of_attribute<0>(v, cm.template beta<2>(h));
 }
 
diff --git a/Combinatorial_map/include/CGAL/Dart.h b/Combinatorial_map/include/CGAL/Dart.h
index 04304ab8780..3d0cea84f4b 100644
--- a/Combinatorial_map/include/CGAL/Dart.h
+++ b/Combinatorial_map/include/CGAL/Dart.h
@@ -103,6 +103,12 @@ namespace CGAL {
     void * & for_compact_container()
     { return mf[0].for_compact_container(); }
 
+    Dart_handle get_f(unsigned int i) const
+    {
+      assert(i<=dimension);
+      return mf[i];
+    }
+    
   protected:
     /** Default constructor: no real initialisation,
      *  because this is done in the combinatorial map class.