diff --git a/Convex_hull_3/include/CGAL/Convex_hull_traits_3.h b/Convex_hull_3/include/CGAL/Convex_hull_traits_3.h
index c115507f45c..e916559a651 100644
--- a/Convex_hull_3/include/CGAL/Convex_hull_traits_3.h
+++ b/Convex_hull_3/include/CGAL/Convex_hull_traits_3.h
@@ -29,6 +29,7 @@
 #include <list>
 #include <CGAL/Filtered_predicate.h>
 #include <CGAL/Cartesian_converter.h>
+#include <CGAL/Default.h>
 
 namespace CGAL {
 template < class R_ >
@@ -185,7 +186,7 @@ struct Convex_hull_traits_base_3<R_, Tag_true>{
 };
 
 
-  template <class R_, class Polyhedron = Polyhedron_3<R_>, class Has_filtered_predicates_tag = Tag_false>
+  template <class R_, class Polyhedron = Default, class Has_filtered_predicates_tag = Tag_false>
 class Convex_hull_traits_3 :
   public Convex_hull_traits_base_3<R_, Has_filtered_predicates_tag>
 {
@@ -198,7 +199,7 @@ class Convex_hull_traits_3 :
   typedef Point_triple<R>                        Plane_3;
   typedef typename R::Vector_3                   Vector_3;
 
-  typedef Polyhedron                             Polyhedron_3;
+  typedef typename Default::Get<Polyhedron, Polyhedron_3<R> >::type Polyhedron_3;
 
   typedef typename R::Construct_segment_3        Construct_segment_3;
   typedef typename R::Construct_ray_3            Construct_ray_3;
diff --git a/Convex_hull_3/include/CGAL/convex_hull_3.h b/Convex_hull_3/include/CGAL/convex_hull_3.h
index c70a95f2400..69dc15d145a 100644
--- a/Convex_hull_3/include/CGAL/convex_hull_3.h
+++ b/Convex_hull_3/include/CGAL/convex_hull_3.h
@@ -71,7 +71,7 @@ struct Default_traits_for_Chull_3{
 //FT is a floating point type and Kernel is a filtered kernel
 template <class Point_3>
 struct Default_traits_for_Chull_3<Point_3,boost::true_type,Tag_true>{
-  typedef Convex_hull_traits_3< typename Kernel_traits<Point_3>::Kernel, Tag_true > type;
+  typedef Convex_hull_traits_3< typename Kernel_traits<Point_3>::Kernel, Default, Tag_true > type;
 };
 
 template <class Traits>
@@ -79,9 +79,9 @@ struct Default_polyhedron_for_Chull_3{
   typedef CGAL::Polyhedron_3<Traits> type;
 };
 
-template <class K,class Tag>
-struct Default_polyhedron_for_Chull_3<Convex_hull_traits_3<K, Tag> >{
-  typedef typename  Convex_hull_traits_3<K, Tag>::Polyhedron_3 type;
+template <class K, class P, class Tag>
+struct Default_polyhedron_for_Chull_3<Convex_hull_traits_3<K, P, Tag> >{
+  typedef typename  Convex_hull_traits_3<K, P, Tag>::Polyhedron_3 type;
 };
  
 //utility class to select the right version of internal predicate Is_on_positive_side_of_plane_3
@@ -130,11 +130,11 @@ public:
 //The main operator() first tries the static version of the predicate, then uses
 //interval arithmetic (the protector must be created before using this predicate)
 //and in case of failure, exact arithmetic is used.
-template <class Kernel>
-class Is_on_positive_side_of_plane_3<Convex_hull_traits_3<Kernel, Tag_true>,Tag_true>{
-  typedef Simple_cartesian<CGAL::internal::Exact_field_selector<double>::Type>         PK;
+template <class Kernel, class P>
+class Is_on_positive_side_of_plane_3<Convex_hull_traits_3<Kernel, P, Tag_true>,Tag_true>{
+  typedef Simple_cartesian<CGAL::internal::Exact_field_selector<double>::Type>  PK;
   typedef Simple_cartesian<Interval_nt_advanced >                               CK;  
-  typedef Convex_hull_traits_3<Kernel, Tag_true>                                Traits;
+  typedef Convex_hull_traits_3<Kernel, P, Tag_true>                             Traits;
   typedef typename Traits::Point_3                                              Point_3;
   
   Cartesian_converter<Kernel,CK>                        to_CK;
@@ -616,6 +616,7 @@ ch_quickhull_polyhedron_3(std::list<typename Traits::Point_3>& points,
   typedef Triangulation_data_structure_2<
     Triangulation_vertex_base_with_info_2<int, GT3_for_CH3<Traits> >,
     Convex_hull_face_base_2<int, Traits> >                           Tds;
+
   typedef typename Tds::Vertex_handle                     Vertex_handle;
   typedef typename Tds::Face_handle                     Face_handle;
 
@@ -685,6 +686,7 @@ ch_quickhull_polyhedron_3(std::list<typename Traits::Point_3>& points,
 
 } } //namespace internal::Convex_hull_3
 
+
 template <class InputIterator, class Traits>
 void
 convex_hull_3(InputIterator first, InputIterator beyond, 
@@ -768,7 +770,8 @@ convex_hull_3(InputIterator first, InputIterator beyond,
   }
 
   // result will be a polyhedron
-  typename internal::Convex_hull_3::Default_polyhedron_for_Chull_3<Traits>::type P;
+  typedef typename internal::Convex_hull_3::Default_polyhedron_for_Chull_3<Traits>::type Polyhedron;
+  Polyhedron P;
 
   P3_iterator minx, maxx, miny, it;
   minx = maxx = miny = it = points.begin();
@@ -783,14 +786,18 @@ convex_hull_3(InputIterator first, InputIterator beyond,
   } else {
     internal::Convex_hull_3::ch_quickhull_polyhedron_3(points, point1_it, point2_it, point3_it, P, traits);
   }
-  CGAL_assertion(P.size_of_vertices()>=3);
-  if (boost::next(P.vertices_begin(),3) == P.vertices_end()){
+  CGAL_assertion(num_vertices(P)>=3);
+  boost::graph_traits<Polyhedron>::halfedge_iterator b,e;
+  boost::tie(b,e) = halfedges(P);
+  if (boost::next(b,3) == e){
+    typename boost::property_map<Polyhedron, vertex_point_t>::type vpmap  = get(CGAL::vertex_point, P);
     typedef typename Traits::Triangle_3                Triangle_3;
     typename Traits::Construct_triangle_3 construct_triangle =
            traits.construct_triangle_3_object();
-    Triangle_3 tri = construct_triangle(P.halfedges_begin()->vertex()->point(), 
-                                        P.halfedges_begin()->next()->vertex()->point(),
-                                        P.halfedges_begin()->opposite()->vertex()->point());
+    
+    Triangle_3 tri = construct_triangle(get(vpmap, target(*b,P)), 
+                                        get(vpmap, target(next(*b,P),P)),
+                                        get(vpmap, target(opposite(*b,P),P)));
     ch_object = make_object(tri);
   }
   else
diff --git a/Convex_hull_3/include/CGAL/convexity_check_3.h b/Convex_hull_3/include/CGAL/convexity_check_3.h
index a4ea10f0951..6dccc4f1c38 100644
--- a/Convex_hull_3/include/CGAL/convexity_check_3.h
+++ b/Convex_hull_3/include/CGAL/convexity_check_3.h
@@ -87,7 +87,10 @@ bool is_strongly_convex_3(const Polyhedron& P, const Traits& traits)
  
   typename boost::property_map<Polyhedron, vertex_point_t>::const_type vpmap  = get(CGAL::vertex_point, P);
 
-  if (P.vertices_begin() == P.vertices_end()) return false;
+  vertex_iterator v_it, v_it_e;
+  boost::tie(v_it, v_it_e) = vertices(P);
+
+  if (v_it == v_it_e) return false;
   
   BOOST_FOREACH(face_descriptor fd , faces(P))
     if (!is_locally_convex(P, vpmap, fd, traits)) 
@@ -98,9 +101,6 @@ bool is_strongly_convex_3(const Polyhedron& P, const Traits& traits)
  
   typename Traits::Coplanar_3 coplanar = traits.coplanar_3_object();
 
-  vertex_iterator v_it, v_it_e;
-  boost::tie(v_it, v_it_e) = vertices(P);
-
   face_iterator f_it, f_it_e;
   boost::tie(f_it, f_it_e) = faces(P);
   Point_3 p;
diff --git a/Convex_hull_3/test/Convex_hull_3/quick_hull_default_traits.cpp b/Convex_hull_3/test/Convex_hull_3/quick_hull_default_traits.cpp
index 6a776bba4c7..2b30ca6857e 100644
--- a/Convex_hull_3/test/Convex_hull_3/quick_hull_default_traits.cpp
+++ b/Convex_hull_3/test/Convex_hull_3/quick_hull_default_traits.cpp
@@ -25,7 +25,7 @@ int main()
   CGAL_static_assertion( (boost::is_same<SCD,Default_traits_for_Chull_3<SCD::Point_3>::type>::value) );
   CGAL_static_assertion( (boost::is_same<SCR,Default_traits_for_Chull_3<SCR::Point_3>::type>::value) );
   CGAL_static_assertion( (boost::is_same<EPEC,Default_traits_for_Chull_3<EPEC::Point_3>::type>::value) );
-  CGAL_static_assertion( (boost::is_same<CGAL::Convex_hull_traits_3<EPIC, CGAL::Tag_true>,Default_traits_for_Chull_3<EPIC::Point_3>::type>::value) );
-  CGAL_static_assertion( (boost::is_same<Is_on_positive_side_of_plane_3<CGAL::Convex_hull_traits_3<EPIC, CGAL::Tag_true> >::Protector,CGAL::Protect_FPU_rounding<true> >::value) );
+  CGAL_static_assertion( (boost::is_same<CGAL::Convex_hull_traits_3<EPIC, CGAL::Default, CGAL::Tag_true>,Default_traits_for_Chull_3<EPIC::Point_3>::type>::value) );
+  CGAL_static_assertion( (boost::is_same<Is_on_positive_side_of_plane_3<CGAL::Convex_hull_traits_3<EPIC, CGAL::Default, CGAL::Tag_true> >::Protector,CGAL::Protect_FPU_rounding<true> >::value) );
   return 0;
 }
diff --git a/Convex_hull_3/test/Convex_hull_3/quickhull_degenerate_test_3.cpp b/Convex_hull_3/test/Convex_hull_3/quickhull_degenerate_test_3.cpp
index 1ace68497a6..9c96fc1a724 100644
--- a/Convex_hull_3/test/Convex_hull_3/quickhull_degenerate_test_3.cpp
+++ b/Convex_hull_3/test/Convex_hull_3/quickhull_degenerate_test_3.cpp
@@ -151,6 +151,9 @@ void test_collinear()
 
 }
 
+#include <CGAL/Triangulation_face_base_with_info_2.h>
+
+
 int main()
 {
   std::vector<Point_3> points;
diff --git a/Hash_map/include/CGAL/Handle_hash_function.h b/Hash_map/include/CGAL/Handle_hash_function.h
index 61a1790390b..25f33979a7e 100644
--- a/Hash_map/include/CGAL/Handle_hash_function.h
+++ b/Hash_map/include/CGAL/Handle_hash_function.h
@@ -31,6 +31,7 @@
 
 namespace CGAL {
 
+
 //mechanism to abuse Handle_hash_function which is the default
 //template parameter of Unique_hash_map
 namespace internal{
diff --git a/Triangulation_3/include/CGAL/star_to_face_graph.h b/Triangulation_3/include/CGAL/star_to_face_graph.h
index 2980017b6f4..a4272b01986 100644
--- a/Triangulation_3/include/CGAL/star_to_face_graph.h
+++ b/Triangulation_3/include/CGAL/star_to_face_graph.h
@@ -32,7 +32,7 @@ namespace CGAL {
 
 
 template<class Triangulation_3,class FG>
-typename boost::graph_trait<FG>::vertex_descriptor
+typename boost::graph_traits<FG>::vertex_descriptor
 star_to_face_graph(const Triangulation_3& t,
                    typename Triangulation_3::Vertex_handle vh,
                    FG& fg,