diff --git a/AABB_tree/include/CGAL/AABB_face_graph_triangle_primitive.h b/AABB_tree/include/CGAL/AABB_face_graph_triangle_primitive.h
index 899d488a06b..7d4a51a367d 100644
--- a/AABB_tree/include/CGAL/AABB_face_graph_triangle_primitive.h
+++ b/AABB_tree/include/CGAL/AABB_face_graph_triangle_primitive.h
@@ -23,8 +23,7 @@
 #define CGAL_AABB_FACE_GRAPH_TRIANGLE_PRIMITIVE_H
 
 #include <CGAL/AABB_primitive.h>
-#include <CGAL/Polyhedron_3.h>
-#include <CGAL/Polyhedron_3_property_map.h>
+#include <CGAL/internal/AABB_tree/Halfedge_and_face_graph_property_maps.h>
 #include <CGAL/Default.h>
 #include <boost/mpl/has_xxx.hpp>
 
diff --git a/AABB_tree/include/CGAL/AABB_halfedge_graph_segment_primitive.h b/AABB_tree/include/CGAL/AABB_halfedge_graph_segment_primitive.h
index fb9ce35bb73..998c2de6969 100644
--- a/AABB_tree/include/CGAL/AABB_halfedge_graph_segment_primitive.h
+++ b/AABB_tree/include/CGAL/AABB_halfedge_graph_segment_primitive.h
@@ -23,8 +23,7 @@
 #define CGAL_AABB_HALFEDGE_GRAPH_SEGMENT_PRIMITIVE_H
 
 #include <CGAL/AABB_primitive.h>
-#include <CGAL/Polyhedron_3.h>
-#include <CGAL/Polyhedron_3_property_map.h>
+#include <CGAL/internal/AABB_tree/Halfedge_and_face_graph_property_maps.h>
 
 #include <iterator>
 #include <boost/mpl/and.hpp>
diff --git a/AABB_tree/include/CGAL/internal/AABB_tree/Halfedge_and_face_graph_property_maps.h b/AABB_tree/include/CGAL/internal/AABB_tree/Halfedge_and_face_graph_property_maps.h
new file mode 100644
index 00000000000..b91ec19c60c
--- /dev/null
+++ b/AABB_tree/include/CGAL/internal/AABB_tree/Halfedge_and_face_graph_property_maps.h
@@ -0,0 +1,197 @@
+// Copyright (c) 2012 GeometryFactory (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
+// 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)     : Sebastien Loriot
+//
+
+#ifndef HALFEDGE_AND_FACE_GRAPH_PROPERTY_MAPS_H
+#define HALFEDGE_AND_FACE_GRAPH_PROPERTY_MAPS_H
+
+#include <CGAL/property_map.h>
+#include <boost/type_traits/is_const.hpp>
+#include <boost/mpl/if.hpp>
+#include <boost/type_traits/remove_const.hpp>
+
+namespace CGAL{
+
+//property map
+template <class FaceGraph,
+           class VertexPointPMap >
+struct Triangle_from_face_descriptor_property_map{
+  typename boost::remove_const<FaceGraph>::type* m_graph;
+  VertexPointPMap m_vppm;
+
+  Triangle_from_face_descriptor_property_map() : m_graph(NULL)
+  {}
+
+  Triangle_from_face_descriptor_property_map(FaceGraph* g)
+    : m_graph( const_cast<typename boost::remove_const<FaceGraph>::type*>(g) ),
+      m_vppm( get(vertex_point, *m_graph) )
+  {}
+
+  Triangle_from_face_descriptor_property_map(FaceGraph* g,
+                                          VertexPointPMap vppm )
+    : m_graph(const_cast<typename boost::remove_const<FaceGraph>::type*>(g)),
+      m_vppm(vppm)
+  {}
+
+  typedef typename boost::property_traits< VertexPointPMap >::value_type Point_3;
+  typedef typename Kernel_traits<Point_3>::Kernel::Triangle_3 Triangle_3;
+ 
+  //classical typedefs
+  typedef typename boost::graph_traits<FaceGraph>::face_descriptor key_type;
+  typedef Triangle_3 value_type;
+  typedef value_type reference;
+  typedef boost::readable_property_map_tag category;
+
+  //get function for property map
+  inline friend
+  Triangle_3
+  get(const Triangle_from_face_descriptor_property_map<FaceGraph,VertexPointPMap>& pmap,
+      typename Triangle_from_face_descriptor_property_map<FaceGraph,VertexPointPMap>::key_type f)
+  {
+    typedef typename boost::property_traits< VertexPointPMap >::value_type Point_3;
+    typedef typename Kernel_traits<Point_3>::Kernel::Triangle_3 Triangle_3;
+    typename boost::remove_const<FaceGraph>::type & g = *(pmap.m_graph);
+
+    CGAL_precondition(halfedge(f,g) == next(next(next(halfedge(f,g),g),g),g));
+    const Point_3& a = get(pmap.m_vppm, target(halfedge(f,g),g));
+    const Point_3& b = get(pmap.m_vppm, target(next(halfedge(f,g),g),g));
+    const Point_3& c = get(pmap.m_vppm,target(next(next(halfedge(f,g),g),g),g));
+ 
+    return Triangle_3(a,b,c);
+  }
+};
+
+
+template < class HalfedgeGraph,
+           class VertexPointPMap >
+struct Segment_from_edge_descriptor_property_map{
+
+  Segment_from_edge_descriptor_property_map()
+  {}
+
+Segment_from_edge_descriptor_property_map(HalfedgeGraph* g)
+  : m_graph( const_cast<typename boost::remove_const<HalfedgeGraph>::type*>(g) ),
+    m_vppm( get(vertex_point, *m_graph) )
+  {}
+
+  Segment_from_edge_descriptor_property_map(HalfedgeGraph* g,
+                                            VertexPointPMap vppm )
+    : m_graph( const_cast<typename boost::remove_const<HalfedgeGraph>::type*>(g) ),
+      m_vppm(vppm)
+  {}
+
+  //classical typedefs
+  typedef typename boost::property_traits< VertexPointPMap >::value_type Point;
+  typedef typename boost::graph_traits<HalfedgeGraph>::edge_descriptor key_type;
+  typedef typename Kernel_traits<Point>::Kernel::Segment_3 value_type;
+  typedef value_type reference;
+  typedef boost::readable_property_map_tag category;
+  //data
+  typename boost::remove_const<HalfedgeGraph>::type* m_graph;
+  VertexPointPMap m_vppm;
+
+  //get function for property map
+  inline friend
+  value_type
+  get(Segment_from_edge_descriptor_property_map<HalfedgeGraph,VertexPointPMap> pmap,
+      key_type h)
+  {
+    typedef typename boost::property_traits< VertexPointPMap >::value_type Point;
+    typedef typename Kernel_traits<Point>::Kernel::Segment_3 Segment_3;
+
+    return Segment_3(get(pmap.m_vppm, source(h, *pmap.m_graph) ),
+                     get(pmap.m_vppm, target(h, *pmap.m_graph) ) );
+  }
+};
+
+//property map to access a point from a facet handle
+template <class FaceGraph,
+          class VertexPointPMap>
+struct One_point_from_face_descriptor_property_map{
+
+  One_point_from_face_descriptor_property_map(FaceGraph* g = NULL)
+    : m_graph( const_cast<typename boost::remove_const<FaceGraph>::type*>(g) )
+  {}
+
+  One_point_from_face_descriptor_property_map(FaceGraph* g, VertexPointPMap vppm )
+    : m_graph( const_cast<typename boost::remove_const<FaceGraph>::type*>(g) ),
+      m_vppm(vppm)
+  {}
+
+  typename boost::remove_const<FaceGraph>::type* m_graph;
+  VertexPointPMap m_vppm;
+
+  //classical typedefs
+  typedef typename boost::graph_traits<FaceGraph>::face_descriptor key_type;
+  typedef typename boost::property_traits< VertexPointPMap >::value_type value_type;
+  typedef typename boost::property_traits< VertexPointPMap >::reference reference;
+  typedef boost::lvalue_property_map_tag category;
+
+  //get function for property map
+  inline friend
+  reference
+  get(const One_point_from_face_descriptor_property_map<FaceGraph,VertexPointPMap>& m,
+      key_type f)
+  {
+    return get(m.m_vppm, target(halfedge(f, *m.m_graph), *m.m_graph));
+  }
+};
+
+//property map to access a point from an edge
+template < class HalfedgeGraph,
+           class VertexPointPMap >
+struct Source_point_from_edge_descriptor{
+  Source_point_from_edge_descriptor(
+    HalfedgeGraph* g = NULL ) :
+  m_graph( const_cast<typename boost::remove_const<HalfedgeGraph>::type*>(g) ),
+  m_vppm( get(vertex_point, *m_graph) )
+  {}
+
+  Source_point_from_edge_descriptor(
+    HalfedgeGraph* g,
+    VertexPointPMap vppm ) :
+  m_graph( const_cast<typename boost::remove_const<HalfedgeGraph>::type*>(g) ),
+  m_vppm(vppm)
+  {}
+
+  //classical typedefs
+  typedef typename boost::property_traits< VertexPointPMap >::value_type value_type;
+  typedef typename boost::property_traits< VertexPointPMap >::reference reference;
+  typedef typename boost::graph_traits<HalfedgeGraph>::edge_descriptor key_type;
+  typedef boost::readable_property_map_tag category;
+  //data
+  typename boost::remove_const<HalfedgeGraph>::type* m_graph;
+  VertexPointPMap m_vppm;
+
+  //get function for property map
+  inline friend
+  reference
+  get(Source_point_from_edge_descriptor<HalfedgeGraph,VertexPointPMap> pmap,
+      key_type h)
+  {
+    return  get(vertex_point,
+                       *pmap.m_graph,
+                       source(h, *pmap.m_graph) );
+  }
+};
+
+} //namespace CGAL
+
+#endif //HALFEDGE_AND_FACE_GRAPH_PROPERTY_MAPS_H