diff --git a/Convex_hull_3/doc/Convex_hull_3/CGAL/Extreme_points_traits_adapter_3.h b/Convex_hull_3/doc/Convex_hull_3/CGAL/Extreme_points_traits_adapter_3.h
new file mode 100644
index 00000000000..efea61694ed
--- /dev/null
+++ b/Convex_hull_3/doc/Convex_hull_3/CGAL/Extreme_points_traits_adapter_3.h
@@ -0,0 +1,42 @@
+namespace CGAL {
+
+/*!
+ * \ingroup PkgConvexHull3Traits
+ * 
+ * The class `Extreme_points_traits_adapter_3` serves as a traits class for the function 
+ * `extreme_points_3()`. It permits the use of this function for accessing vertices, indices,
+ * or anything that can be used as `key_type` for `PointPropertyMap`.
+ * 
+ * \tparam Base_traits a model of `ConvexHullTraits_3` and `IsStronglyConvexTraits_3`
+ * \tparam PointPropertyMap a model of `ReadablePropertyMap` with `CGAL::Point_3` 
+ * as value_type.
+ * 
+ * \cgalModels `ConvexHullTraits_3`
+ * \cgalModels `IsStronglyConvexTraits_3` 
+ */
+template<class Base_traits,class PointPropertyMap>
+class Extreme_points_traits_adapter_3
+{
+public:
+  /*!
+   * Constructor for the adapter.
+   * 
+   * It uses the functors from `Base_traits` with a call to `get()` for each argument.
+   * 
+   * \param pmap the propertymap used for retrieving the data.
+   * \param base the base ConvexHullTraits_3 used for `extreme_points_3()`.
+   */
+  Extreme_points_traits_adapter_3(const PointPropertyMap& pmap, Base_traits base=Base_traits());
+  /*!
+   
+   */
+  typedef boost::property_traits<PointPropertyMap>::key_type Point_3;
+ 
+  /*!
+   * \return the `CGAL::Point_3` associated with `k`
+   */
+  boost::property_traits<PointPropertyMap>::reference
+  get_point(const typename boost::property_traits<PointPropertyMap>::key_type& k) const;
+      
+};
+}//end CGAL
diff --git a/Convex_hull_3/doc/Convex_hull_3/CGAL/convex_hull_3.h b/Convex_hull_3/doc/Convex_hull_3/CGAL/convex_hull_3.h
index 560150517ea..f89c03e27ad 100644
--- a/Convex_hull_3/doc/Convex_hull_3/CGAL/convex_hull_3.h
+++ b/Convex_hull_3/doc/Convex_hull_3/CGAL/convex_hull_3.h
@@ -82,6 +82,8 @@ then the default traits class used is `Convex_hull_traits_3<R>`, and `R` otherwi
 @param range the range of input points.
 @param out an output iterator where the extreme points will be put.
 @param traits an instance of `Traits`.
+
+\sa CGAL::Extreme_points_traits_adapter_3
 */
 template <class InputRange, class OutputIterator, class Traits>
 OutputIterator
diff --git a/Convex_hull_3/doc/Convex_hull_3/PackageDescription.txt b/Convex_hull_3/doc/Convex_hull_3/PackageDescription.txt
index 4dbf102b99e..4836390c82f 100644
--- a/Convex_hull_3/doc/Convex_hull_3/PackageDescription.txt
+++ b/Convex_hull_3/doc/Convex_hull_3/PackageDescription.txt
@@ -70,6 +70,7 @@ defining `CGAL_CH_CHECK_EXPENSIVE`.
 ## Traits Classes ##
 
 - `CGAL::Convex_hull_traits_3<R>`
+- `CGAL::Extreme_points_traits_adapter_3`
 
 ## Convex Hull Functions ##
 
diff --git a/Convex_hull_3/include/CGAL/Vertex_to_point_traits_adapter_3.h b/Convex_hull_3/include/CGAL/Extreme_points_traits_adapter_3.h
similarity index 81%
rename from Convex_hull_3/include/CGAL/Vertex_to_point_traits_adapter_3.h
rename to Convex_hull_3/include/CGAL/Extreme_points_traits_adapter_3.h
index 3e90c0f98b0..4cb222b0d10 100644
--- a/Convex_hull_3/include/CGAL/Vertex_to_point_traits_adapter_3.h
+++ b/Convex_hull_3/include/CGAL/Extreme_points_traits_adapter_3.h
@@ -19,8 +19,8 @@
 //
 // Author(s)     : Maxime Gimeno
 
-#ifndef CGAL_VERTEX_TO_POINT_TRAITS_ADAPTER_3_H
-#define CGAL_VERTEX_TO_POINT_TRAITS_ADAPTER_3_H
+#ifndef CGAL_EXTREME_POINTS_TRAITS_ADAPTER_3_H
+#define CGAL_EXTREME_POINTS_TRAITS_ADAPTER_3_H
 
 #include <CGAL/license/Convex_hull_3.h>
 
@@ -38,13 +38,13 @@
 namespace CGAL {
 
 namespace Convex_hull_impl{
-template <class F, class VertexPointMap>
+template <class F, class PointPropertyMap>
 struct Forward_functor
   : public F
 {
-  VertexPointMap vpm_;
+  PointPropertyMap vpm_;
   
-  Forward_functor(const VertexPointMap& vpm,
+  Forward_functor(const PointPropertyMap& vpm,
                   const F& f) : F(f), vpm_(vpm) {}
   
   
@@ -77,27 +77,27 @@ struct Forward_functor
   }
 };
 }//end Convex_hull_impl
-template<class Base_traits,class VertexPointMap>
-class Vertex_to_point_traits_adapter
+template<class Base_traits,class PointPropertyMap>
+class Extreme_points_traits_adapter_3
     :public Base_traits
 {
-  VertexPointMap vpm_;
+  PointPropertyMap vpm_;
   
   
 public:
-  Vertex_to_point_traits_adapter(const VertexPointMap& vpmap, Base_traits base=Base_traits())
+  Extreme_points_traits_adapter_3(const PointPropertyMap& vpmap, Base_traits base=Base_traits())
     :Base_traits(base), vpm_(vpmap)
   {}
-  typedef typename boost::property_traits<VertexPointMap>::key_type Vertex;
+  typedef typename boost::property_traits<PointPropertyMap>::key_type Vertex;
   typedef Vertex Point_3;
-  typedef Convex_hull_impl::Forward_functor<typename Base_traits::Equal_3, VertexPointMap> Equal_3;
-  typedef Convex_hull_impl::Forward_functor<typename Base_traits::Collinear_3, VertexPointMap> Collinear_3;
-  typedef Convex_hull_impl::Forward_functor<typename Base_traits::Coplanar_3, VertexPointMap> Coplanar_3;
-  typedef Convex_hull_impl::Forward_functor<typename Base_traits::Less_distance_to_point_3, VertexPointMap> Less_distance_to_point_3; 
+  typedef Convex_hull_impl::Forward_functor<typename Base_traits::Equal_3, PointPropertyMap> Equal_3;
+  typedef Convex_hull_impl::Forward_functor<typename Base_traits::Collinear_3, PointPropertyMap> Collinear_3;
+  typedef Convex_hull_impl::Forward_functor<typename Base_traits::Coplanar_3, PointPropertyMap> Coplanar_3;
+  typedef Convex_hull_impl::Forward_functor<typename Base_traits::Less_distance_to_point_3, PointPropertyMap> Less_distance_to_point_3; 
   class Less_signed_distance_to_plane_3
       :public Base_traits::Less_signed_distance_to_plane_3
   {  
-    VertexPointMap vpm_;
+    PointPropertyMap vpm_;
     const typename Base_traits::Less_signed_distance_to_plane_3& base;
   public:
     typedef typename Base_traits::Plane_3 Plane_3;
@@ -105,7 +105,7 @@ public:
     typedef bool             result_type;
     
     Less_signed_distance_to_plane_3(
-        const VertexPointMap& map,
+        const PointPropertyMap& map,
         const typename Base_traits::Less_signed_distance_to_plane_3& base):
       Base_traits::Less_signed_distance_to_plane_3(base),vpm_(map), base(base){}
     
@@ -129,10 +129,10 @@ public:
   
   class Construct_plane_3:public Base_traits::Construct_plane_3
   {  
-    VertexPointMap vpm_;
+    PointPropertyMap vpm_;
     const typename Base_traits::Construct_plane_3& base;
   public:
-    Construct_plane_3(const VertexPointMap& map, const typename Base_traits::Construct_plane_3& base):
+    Construct_plane_3(const PointPropertyMap& map, const typename Base_traits::Construct_plane_3& base):
       Base_traits::Construct_plane_3(base),vpm_(map), base(base){}
     typename Base_traits::Plane_3 operator()(const Point_3& p, const Point_3& q, const Point_3& r)const 
     {
@@ -144,10 +144,10 @@ public:
   
   class Has_on_positive_side_3:public Base_traits::Has_on_positive_side_3
   {  
-    VertexPointMap vpm_;
+    PointPropertyMap vpm_;
     const typename Base_traits::Has_on_positive_side_3& base;
   public:
-    Has_on_positive_side_3(const VertexPointMap& map,const typename Base_traits::Has_on_positive_side_3& base):
+    Has_on_positive_side_3(const PointPropertyMap& map,const typename Base_traits::Has_on_positive_side_3& base):
       Base_traits::Has_on_positive_side_3(base),vpm_(map), base(base){}
     
     typedef typename Base_traits::Plane_3          Plane_3;
@@ -166,24 +166,24 @@ public:
   template<class Base_proj_traits>
   class Proj_traits_3:public Base_proj_traits
   {
-    VertexPointMap vpm_;
+    PointPropertyMap vpm_;
     typedef Base_proj_traits Btt;
   public:
-    Proj_traits_3(const VertexPointMap& map,const Btt& base):
+    Proj_traits_3(const PointPropertyMap& map,const Btt& base):
       Base_proj_traits(base),vpm_(map){}
     typedef Point_3 Point_2;
-    typedef Convex_hull_impl::Forward_functor<typename Btt::Equal_2, VertexPointMap> Equal_2;
-    typedef Convex_hull_impl::Forward_functor<typename Btt::Less_xy_2, VertexPointMap> Less_xy_2;
-    typedef Convex_hull_impl::Forward_functor<typename Btt::Less_yx_2, VertexPointMap> Less_yx_2;
-    typedef Convex_hull_impl::Forward_functor<typename Btt::Less_signed_distance_to_line_2, VertexPointMap> Less_signed_distance_to_line_2;
-    typedef Convex_hull_impl::Forward_functor<typename Btt::Left_turn_2, VertexPointMap> Left_turn_2;
+    typedef Convex_hull_impl::Forward_functor<typename Btt::Equal_2, PointPropertyMap> Equal_2;
+    typedef Convex_hull_impl::Forward_functor<typename Btt::Less_xy_2, PointPropertyMap> Less_xy_2;
+    typedef Convex_hull_impl::Forward_functor<typename Btt::Less_yx_2, PointPropertyMap> Less_yx_2;
+    typedef Convex_hull_impl::Forward_functor<typename Btt::Less_signed_distance_to_line_2, PointPropertyMap> Less_signed_distance_to_line_2;
+    typedef Convex_hull_impl::Forward_functor<typename Btt::Left_turn_2, PointPropertyMap> Left_turn_2;
     
     class Less_rotate_ccw_2:public Btt::Less_rotate_ccw_2
     {
-      VertexPointMap vpm_;
+      PointPropertyMap vpm_;
       const typename Btt::Less_rotate_ccw_2& base;
     public:
-      Less_rotate_ccw_2(const VertexPointMap& map,const typename Btt::Less_rotate_ccw_2& base):
+      Less_rotate_ccw_2(const PointPropertyMap& map,const typename Btt::Less_rotate_ccw_2& base):
         Btt::Less_rotate_ccw_2(base),vpm_(map), base(base){}
     public:      
       bool operator()(Point_2 e, Point_2 p,Point_2 q) const
@@ -203,10 +203,10 @@ public:
     
     class Orientation_2:public Btt::Orientation_2
     {
-      VertexPointMap vpm_;                                                           
+      PointPropertyMap vpm_;                                                           
       const typename Btt::Orientation_2& base;                                   
     public:                                                                          
-      Orientation_2(const VertexPointMap& map,const typename Btt::Orientation_2& base):
+      Orientation_2(const PointPropertyMap& map,const typename Btt::Orientation_2& base):
         Btt::Orientation_2(base),vpm_(map), base(base){}                         
       
       typename CGAL::Orientation operator()(Point_2 e,Point_2 p, Point_2 q) const                                    
@@ -228,8 +228,8 @@ public:
   Traits_xz_3 construct_traits_xz_3_object()const
   {return Traits_xz_3(vpm_, static_cast<const Base_traits*>(this)->construct_traits_xz_3_object());}
 
-  typename boost::property_traits<VertexPointMap>::reference
-  get_point(const typename boost::property_traits<VertexPointMap>::key_type& k) const
+  typename boost::property_traits<PointPropertyMap>::reference
+  get_point(const typename boost::property_traits<PointPropertyMap>::key_type& k) const
   {
     return get(vpm_, k);
   }
@@ -238,4 +238,4 @@ public:
 
 }//end CGAL
 
-#endif // CGAL_VERTEX_TO_POINT_TRAITS_ADAPTER_3_H
+#endif // CGAL_EXTREME_POINTS_TRAITS_ADAPTER_3_H
diff --git a/Convex_hull_3/include/CGAL/convex_hull_3.h b/Convex_hull_3/include/CGAL/convex_hull_3.h
index db34e478207..46331127bcd 100644
--- a/Convex_hull_3/include/CGAL/convex_hull_3.h
+++ b/Convex_hull_3/include/CGAL/convex_hull_3.h
@@ -68,7 +68,7 @@
 namespace CGAL {
 
 // Forward declaration
-template<class Base_traits,class VertexPointMap> class Vertex_to_point_traits_adapter;
+template<class Base_traits,class VertexPointMap> class Extreme_points_traits_adapter_3;
 
 namespace internal{  namespace Convex_hull_3{
 
@@ -206,10 +206,10 @@ public:
 };
 
 template <class Base_traits, class VPM, class Is_CK>
-class Is_on_positive_side_of_plane_3< Vertex_to_point_traits_adapter<Base_traits, VPM>, Is_CK>
+class Is_on_positive_side_of_plane_3< Extreme_points_traits_adapter_3<Base_traits, VPM>, Is_CK>
   : public Is_on_positive_side_of_plane_3< Base_traits >
 {
-  typedef Vertex_to_point_traits_adapter<Base_traits, VPM> Traits;
+  typedef Extreme_points_traits_adapter_3<Base_traits, VPM> Traits;
   typedef Is_on_positive_side_of_plane_3< Base_traits > Base;
   typedef typename Traits::Point_3 Point_3;
   const Traits& m_traits;
@@ -1033,28 +1033,11 @@ extreme_vertices(const InputRange& range,
                  const Traits& traits)
 {
   
-  Vertex_to_point_traits_adapter<Traits, PointPropertyMap> traits_adapter(map, traits);
+  Extreme_points_traits_adapter_3<Traits, PointPropertyMap> traits_adapter(map, traits);
   extreme_points_3(range, out,traits_adapter);
   return out;
 }
 
-template <class InputRange,
-          class PointPropertyMap,
-          class OutputIterator>
-OutputIterator
-extreme_vertices(const InputRange& range,
-                 PointPropertyMap map, 
-                 OutputIterator out)
-{
-  typedef typename boost::property_traits<PointPropertyMap>::value_type Point_3;
-  typedef typename internal::Convex_hull_3::Default_traits_for_Chull_3<Point_3>::type Traits;
-  
-  Vertex_to_point_traits_adapter<Traits, PointPropertyMap> traits_adapter(map, Traits());
-  extreme_points_3(range, out,traits_adapter);
-  return out;
-}
-
-
 template <class InputIterator, class Polyhedron_3>
 void convex_hull_3(InputIterator first, InputIterator beyond,
                    Polyhedron_3& polyhedron)
diff --git a/Convex_hull_3/test/Convex_hull_3/test_extreme_points.cpp b/Convex_hull_3/test/Convex_hull_3/test_extreme_points.cpp
index 9fd608ad397..cd7fc7f3d3b 100644
--- a/Convex_hull_3/test/Convex_hull_3/test_extreme_points.cpp
+++ b/Convex_hull_3/test/Convex_hull_3/test_extreme_points.cpp
@@ -1,8 +1,8 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Surface_mesh.h>
 #include <CGAL/convex_hull_3.h>
-#include <CGAL/Vertex_to_point_traits_adapter_3.h>
 #include <CGAL/Convex_hull_traits_3.h>
+#include <CGAL/Extreme_points_traits_adapter_3.h>
 #include <CGAL/Exact_rational.h>
 #include <CGAL/Cartesian.h>
 #include <CGAL/Polyhedron_3.h>
@@ -212,9 +212,12 @@ void test_extreme_vertices(const char* fname)
     std::cerr << fname << " is not a valid off file.\n";
     exit(1);
   }  
+  CGAL::Extreme_points_traits_adapter_3<CGAL::Convex_hull_traits_3<K, Polyhedron_3, CGAL::Tag_true>
+      ,boost::property_map<Polyhedron_3, CGAL::vertex_point_t>::type >
+      traits(get(CGAL::vertex_point, P));
   std::vector<boost::graph_traits<Polyhedron_3>::vertex_descriptor> verts;
-  CGAL::extreme_vertices(vertices(P), get(CGAL::vertex_point, P), std::back_inserter(verts) ,
-                   CGAL::Convex_hull_traits_3<K, Polyhedron_3, CGAL::Tag_true>());
+  CGAL::extreme_points_3(vertices(P), std::back_inserter(verts) ,
+                   traits);
 }
 
 int main()