diff --git a/Polyhedron/demo/Polyhedron/Polyhedron_demo_mesh_simplification_plugin.cpp b/Polyhedron/demo/Polyhedron/Polyhedron_demo_mesh_simplification_plugin.cpp
index bdad534c43c..e6881669c49 100644
--- a/Polyhedron/demo/Polyhedron/Polyhedron_demo_mesh_simplification_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Polyhedron_demo_mesh_simplification_plugin.cpp
@@ -68,8 +68,8 @@ void Polyhedron_demo_mesh_simplification_plugin::on_actionSimplify_triggered()
     namespace SMS = CGAL::Surface_mesh_simplification;
     SMS::Count_stop_predicate< Polyhedron > stop(nb_edges); // target #edges
     SMS::edge_collapse( *pMesh, stop,
-      CGAL::vertex_index_map(boost::get(CGAL::vertex_external_index,*pMesh))
-      .edge_index_map(boost::get(CGAL::edge_external_index,*pMesh)));
+      CGAL::vertex_index_map(get(CGAL::vertex_external_index,*pMesh))
+      .halfedge_index_map(get(CGAL::halfedge_external_index,*pMesh)));
     std::cout << "ok (" << time.elapsed() << " ms, " 
       << pMesh->size_of_halfedges() / 2 << " edges)" << std::endl;
 
diff --git a/Polyhedron/demo/Polyhedron/Scene_polyhedron_item.cpp b/Polyhedron/demo/Polyhedron/Scene_polyhedron_item.cpp
index 82b13546f1b..76308e61bbe 100644
--- a/Polyhedron/demo/Polyhedron/Scene_polyhedron_item.cpp
+++ b/Polyhedron/demo/Polyhedron/Scene_polyhedron_item.cpp
@@ -28,8 +28,8 @@ Input_facets_AABB_tree* get_aabb_tree(Scene_polyhedron_item* item)
     Polyhedron* poly = item->polyhedron();
     if(poly) {
       Input_facets_AABB_tree* tree = 
-        new Input_facets_AABB_tree(poly->facets_begin(),
-                                   poly->facets_end(),
+        new Input_facets_AABB_tree(faces(*poly).first,
+                                   faces(*poly).second,
                                    *poly);
       item->setProperty(aabb_property_name, 
                         QVariant::fromValue<void*>(tree));
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/Edge_collapse.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/Edge_collapse.h
index 3e9e53ea8c7..e932cece521 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/Edge_collapse.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/Edge_collapse.h
@@ -71,7 +71,8 @@ public:
   typedef typename GraphTraits::edges_size_type        size_type ;
   
   typedef typename GraphTraits::edge_iterator edge_iterator ;
-  typedef typename ECM::Vertex::Point                    Point ;
+  typedef typename boost::property_map<ECM, CGAL::vertex_point_t>::type Vertex_point_pmap;
+  typedef typename boost::property_traits<Vertex_point_pmap>::value_type Point;
 
   typedef typename GetCost     ::result_type Cost_type ;
   typedef typename GetPlacement::result_type Placement_type ;
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Edge_collapse_visitor_base.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Edge_collapse_visitor_base.h
index b8728964435..c9781387c6f 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Edge_collapse_visitor_base.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Edge_collapse_visitor_base.h
@@ -38,7 +38,8 @@ struct Edge_collapse_visitor_base
   
   typedef typename GraphTraits::edges_size_type   size_type ;
   typedef typename GraphTraits::vertex_descriptor vertex_descriptor ;
-  typedef typename ECM::Vertex::Point     Point ;
+  typedef typename boost::property_map<ECM, CGAL::vertex_point_t>::type Vertex_point_pmap;
+  typedef typename boost::property_traits<Vertex_point_pmap>::value_type Point;
   typedef typename Kernel_traits<Point>::Kernel   Kernel ;
   typedef typename Kernel::FT                     FT ;
   
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Count_ratio_stop_predicate.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Count_ratio_stop_predicate.h
index 23a9891b9e9..18bc0502e10 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Count_ratio_stop_predicate.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Count_ratio_stop_predicate.h
@@ -50,7 +50,8 @@ public:
   typedef typename boost::graph_traits<ECM>::edge_descriptor edge_descriptor ;
   typedef typename boost::graph_traits<ECM>::edges_size_type size_type ;
   
-  typedef typename ECM::Vertex::Point Point ;
+  typedef typename boost::property_map<ECM, CGAL::vertex_point_t>::type Vertex_point_pmap;
+  typedef typename boost::property_traits<Vertex_point_pmap>::value_type Point;
   typedef typename Kernel_traits<Point>::Kernel      Kernel ;
   typedef typename Kernel::FT                        FT ;
   
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Count_stop_predicate.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Count_stop_predicate.h
index 09406683be4..c9c403db111 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Count_stop_predicate.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Count_stop_predicate.h
@@ -49,7 +49,8 @@ public:
   
 private :
 
-  typedef typename ECM::Vertex::Point Point ;
+  typedef typename boost::property_map<ECM, CGAL::vertex_point_t>::type Vertex_point_pmap;
+  typedef typename boost::property_traits<Vertex_point_pmap>::value_type Point;
   typedef typename Kernel_traits<Point>::Kernel      Kernel ;
 
 public :
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Detail/Lindstrom_Turk_core.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Detail/Lindstrom_Turk_core.h
index 2da0d196935..0a637c9eefc 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Detail/Lindstrom_Turk_core.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Detail/Lindstrom_Turk_core.h
@@ -41,7 +41,7 @@ namespace CGAL {
 namespace Surface_mesh_simplification
 {
 
-  template<class ECM_, class Kernel_ = typename Kernel_traits< typename ECM_::Vertex::Point>::Kernel >
+  template<class ECM_, class Kernel_ = typename Kernel_traits<typename boost::property_traits<typename boost::property_map<ECM_, CGAL::vertex_point_t>::type>::value_type>::Kernel >
 class LindstromTurkCore
 {
 public:
@@ -61,7 +61,8 @@ public:
   
   typedef typename Kernel::Point_3 Point ;
 
-  typedef typename ECM::Vertex::Point ECM_Point ;
+  typedef typename boost::property_map<ECM, CGAL::vertex_point_t>::type Vertex_point_pmap;
+  typedef typename boost::property_traits<Vertex_point_pmap>::value_type ECM_Point;
   
   typedef typename Kernel_traits<ECM_Point>::Kernel ECM_Kernel ;
   
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Edge_length_cost.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Edge_length_cost.h
index 208e69a923c..eaf7ef3137b 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Edge_length_cost.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Edge_length_cost.h
@@ -40,8 +40,9 @@ public:
   
   typedef Edge_profile<ECM> Profile ;
   
-  typedef typename ECM::Vertex::Point Point ;
-  
+  typedef typename boost::property_map<ECM, CGAL::vertex_point_t>::type Vertex_point_pmap;
+  typedef typename boost::property_traits<Vertex_point_pmap>::value_type Point;
+ 
   typedef typename Kernel_traits<Point>::Kernel Kernel ;
 
   typedef typename Kernel::FT FT ;
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Edge_profile.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Edge_profile.h
index 7685e662e00..6a5e401b9a7 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Edge_profile.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Edge_profile.h
@@ -44,7 +44,8 @@ public:
   typedef typename GraphTraits::vertex_descriptor vertex_descriptor ;
   typedef typename GraphTraits::halfedge_descriptor   halfedge_descriptor ;
 
-  typedef typename ECM::Vertex::Point Point ;
+  typedef typename boost::property_map<ECM, CGAL::vertex_point_t>::type Vertex_point_pmap;
+  typedef typename boost::property_traits<Vertex_point_pmap>::value_type Point;
     
 public:
 
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/LindstromTurk_cost.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/LindstromTurk_cost.h
index c5aaa6d5655..f81f462beae 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/LindstromTurk_cost.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/LindstromTurk_cost.h
@@ -36,7 +36,9 @@ public:
 
   typedef Edge_profile<ECM> Profile ;
      
-  typedef typename ECM::Vertex::Point Point ;
+  typedef typename boost::property_map<ECM, CGAL::vertex_point_t>::type Vertex_point_pmap;
+  typedef typename boost::property_traits<Vertex_point_pmap>::value_type Point;
+ 
   typedef typename Kernel_traits<Point>::Kernel      Kernel ;
   typedef typename Kernel::FT                        FT ;
   
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/LindstromTurk_placement.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/LindstromTurk_placement.h
index 9b72b1649a5..87af1f46499 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/LindstromTurk_placement.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/LindstromTurk_placement.h
@@ -36,8 +36,9 @@ public:
   
   typedef Edge_profile<ECM> Profile ;
   
-  typedef typename ECM::Vertex::Point Point ;
-
+  typedef typename boost::property_map<ECM, CGAL::vertex_point_t>::type Vertex_point_pmap;
+  typedef typename boost::property_traits<Vertex_point_pmap>::value_type Point;
+ 
   typedef optional<Point> result_type ;
 
 public:
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Midpoint_placement.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Midpoint_placement.h
index d3147edca51..cee5e997b73 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Midpoint_placement.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Midpoint_placement.h
@@ -36,8 +36,9 @@ public:
   
   typedef Edge_profile<ECM> Profile ;
   
-  typedef typename ECM::Vertex::Point Point ;
-  
+  typedef typename boost::property_map<ECM, CGAL::vertex_point_t>::type Vertex_point_pmap;
+  typedef typename boost::property_traits<Vertex_point_pmap>::value_type Point;
+   
   typedef optional<Point> result_type ;
     
 public: