diff --git a/Orthtree/include/CGAL/Orthtree_traits_face_graph.h b/Orthtree/include/CGAL/Orthtree_traits_face_graph.h
index 948e5525e98..bbdd2ac7c15 100644
--- a/Orthtree/include/CGAL/Orthtree_traits_face_graph.h
+++ b/Orthtree/include/CGAL/Orthtree_traits_face_graph.h
@@ -15,6 +15,8 @@
 
 #include <CGAL/license/Orthtree.h>
 
+#include <CGAL/Orthtree_traits_3_base.h>
+
 #include <CGAL/Dimension.h>
 #include <CGAL/Bbox_3.h>
 
@@ -23,25 +25,28 @@ namespace CGAL
 
 template <class PolygonMesh, class VPM>
 struct Orthtree_traits_face_graph
-{
+  : public Orthtree_traits_3_base<typename Kernel_traits<typename boost::property_traits<VPM>::value_type>::type> {
+
   Orthtree_traits_face_graph(const PolygonMesh& pm, VPM vpm)
-    : m_pm(pm)
-    , m_vpm(vpm)
-  {}
+    : m_pm(pm), m_vpm(vpm) {}
 
+  using Self = Orthtree_traits_face_graph<PolygonMesh, VPM>;
+  using Tree = Orthtree<Self>;
+
+  using Point_d = typename Self::Point_d;
+  using Dimension = typename Self::Dimension;
+  using Bbox_d = typename Self::Bbox_d;
+  using FT = typename Self::FT;
+  using Sphere_d = typename Self::Sphere_d; // SL: why?
+  using Array = typename Self::Array; // SL: why?
+  using Cartesian_const_iterator_d = typename Self::Cartesian_const_iterator_d;
 
-  using Point_d = typename boost::property_traits<VPM>::value_type;
-  using Geom_traits = typename Kernel_traits<Point_d>::type;
-  using Dimension = Dimension_tag<3>;
-  using Bbox_d = Bbox_3;
-  using FT = typename Geom_traits::FT;
-  using Sphere_d = typename Geom_traits::Sphere_3; // SL: why?
-  using Array = std::array<FT, 3>; // SL: why?
-  using Cartesian_const_iterator_d = typename Geom_traits::Cartesian_const_iterator_3;
   // SL: these could be considered as built-in data and if the typedefs are not present, the tree have none
   using Node_data_element = typename boost::graph_traits<PolygonMesh>::face_descriptor;
   using Node_data = std::vector<Node_data_element>;
 
+  using Geom_traits = typename Kernel_traits<Point_d>::type;
+
   struct Construct_bbox_d {
     Bbox_d operator()(const Array& min,
                       const Array& max) const {
@@ -59,64 +64,57 @@ struct Orthtree_traits_face_graph
   Construct_point_d_from_array construct_point_d_from_array_object() const { return Construct_point_d_from_array(); }
   Construct_bbox_d construct_bbox_d_object() const { return Construct_bbox_d(); }
 
-  // SL: why in each traits? because it's dimension dependant?
-  enum Adjacency {
-    LEFT,
-    RIGHT,
-    DOWN,
-    UP,
-    BACK,
-    FRONT
-  };
+  auto root_node_bbox_object() const {
+    return [&]() -> std::pair<Array, Array> {
 
-  std::pair<Array, Array> root_node_bbox() const
-  {
-    Array min={0.0,0}, max={0.0,0};
-    if (faces(m_pm).begin()!=faces(m_pm).end())
-    {
-      const Point_d& p = get(m_vpm, *vertices(m_pm).begin());
-      min={p.x(), p.y(), p.z()};
-      max=min;
-      for (auto v : vertices(m_pm))
+      Array min={0.0,0}, max={0.0,0};
+      if (faces(m_pm).begin()!=faces(m_pm).end())
       {
-        const Point_d& p_v = get(m_vpm, v);
-        for (int i=0; i<3; ++i)
+        const Point_d& p = get(m_vpm, *vertices(m_pm).begin());
+        min={p.x(), p.y(), p.z()};
+        max=min;
+        for (auto v : vertices(m_pm))
         {
-          if (p_v[i]<min[i]) min[i]=p_v[i];
-          if (p_v[i]>max[i]) max[i]=p_v[i];
+          const Point_d& p_v = get(m_vpm, v);
+          for (int i=0; i<3; ++i)
+          {
+            if (p_v[i]<min[i]) min[i]=p_v[i];
+            if (p_v[i]>max[i]) max[i]=p_v[i];
+          }
         }
       }
-    }
 
-    return {min, max};
+      return {min, max};
+    };
   }
 
   // SL: not clear to me what it should do from the doc
-  Node_data root_node_contents()
-  {
-    return {faces(m_pm).begin(), faces(m_pm).end()};
+  auto root_node_contents_object() {
+    return [&]() -> Node_data {
+      return {faces(m_pm).begin(), faces(m_pm).end()};
+    };
   }
 
-  template<class NodeIndex, class Tree>
-  void distribute_node_contents(NodeIndex n, Tree &tree, const Point_d &center)
-  {
-    Node_data& ndata = tree.data(n);
-    for (int i=0; i<8; ++i)
-    {
-      NodeIndex child = tree.child(n, i);
-      Node_data& child_data = tree.data(child);
-      Bbox_d bbox = tree.bbox(child);
-      for (Node_data_element f : ndata)
+  auto distribute_node_contents_object(){
+    return [&](typename Tree::Node_index n, Tree &tree, const Point_d &center) -> void {
+      Node_data& ndata = tree.data(n);
+      for (int i=0; i<8; ++i)
       {
-        typename boost::graph_traits<PolygonMesh>::halfedge_descriptor
-          h = halfedge(f, m_pm);
-        typename Geom_traits::Triangle_3 t(get(m_vpm, source(h, m_pm)),
-                                           get(m_vpm, target(h, m_pm)),
-                                           get(m_vpm, target(next(h, m_pm), m_pm)));
-        if(do_intersect(t, bbox))
-          child_data.push_back(f);
+        typename Tree::Node_index child = tree.child(n, i);
+        Node_data& child_data = tree.data(child);
+        Bbox_d bbox = tree.bbox(child);
+        for (Node_data_element f : ndata)
+        {
+          typename boost::graph_traits<PolygonMesh>::halfedge_descriptor
+            h = halfedge(f, m_pm);
+          typename Geom_traits::Triangle_3 t(get(m_vpm, source(h, m_pm)),
+                                             get(m_vpm, target(h, m_pm)),
+                                             get(m_vpm, target(next(h, m_pm), m_pm)));
+          if(do_intersect(t, bbox))
+            child_data.push_back(f);
+        }
       }
-    }
+    };
   }
 
   //SL: I find convenient to put it here