diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Cartesian_base.h b/Cartesian_kernel/include/CGAL/Cartesian/Cartesian_base.h
index 61973aee365..96f3ab93da3 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Cartesian_base.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Cartesian_base.h
@@ -102,8 +102,13 @@ struct Cartesian_base
                                                         Angle;
 
     template <typename T>
-    struct Dimension {
-      static const int value = T::static_dimension;
+    struct Ambiant_dimension {
+      typedef typename T::Ambiant_dimension type;
+    };
+
+    template <typename T>
+    struct Feature_dimension {
+      typedef typename T::Feature_dimension type;
     };
 
     typedef PointC2<Kernel>                             Point_2;
diff --git a/Conic_2/include/CGAL/Conic_2.h b/Conic_2/include/CGAL/Conic_2.h
index 3b679a5fdad..03c3241a9f2 100644
--- a/Conic_2/include/CGAL/Conic_2.h
+++ b/Conic_2/include/CGAL/Conic_2.h
@@ -26,6 +26,7 @@
 #define CGAL_CONIC_2_H
 
 #include <CGAL/Conic_misc.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -39,7 +40,8 @@ class Conic_2 : public R_::Kernel_base::Conic_2 {
 
   public:
 
-    static const int static_dimension = 2;
+    typedef Dimension_tag<2>  Ambiant_dimension;
+    typedef Dimension_tag<1>  Feature_dimension;
 
     // types
     typedef  R_                    R;
diff --git a/Filtered_kernel/include/CGAL/Filtered_kernel.h b/Filtered_kernel/include/CGAL/Filtered_kernel.h
index 7e67db78680..a7ce445f4f2 100644
--- a/Filtered_kernel/include/CGAL/Filtered_kernel.h
+++ b/Filtered_kernel/include/CGAL/Filtered_kernel.h
@@ -68,8 +68,13 @@ struct Filtered_kernel_base
     };
 
     template < typename T >
-    struct Dimension {
-        static const int value = T::static_dimension; // maybe not the right way...
+    struct Ambiant_dimension {
+        typedef typename T::Ambiant_dimension type; // maybe not the right way...
+    };
+
+    template < typename T >
+    struct Feature_dimension {
+        typedef typename T::Feature_dimension type; // maybe not the right way...
     };
 
     // We change the predicates.
diff --git a/Filtered_kernel/include/CGAL/Lazy_kernel.h b/Filtered_kernel/include/CGAL/Lazy_kernel.h
index ef67489490f..b9f927dbb6e 100644
--- a/Filtered_kernel/include/CGAL/Lazy_kernel.h
+++ b/Filtered_kernel/include/CGAL/Lazy_kernel.h
@@ -60,8 +60,13 @@ public:
   struct Base { typedef Lazy_kernel_generic_base<Exact_kernel, Approximate_kernel, E2A, Kernel2>  Type; };
 
   template < typename T >
-  struct Dimension {
-    static const int value = T::static_dimension;
+  struct Ambiant_dimension {
+    typedef typename T::Ambiant_dimension type;
+  };
+
+  template < typename T >
+  struct Feature_dimension {
+    typedef typename T::Feature_dimension type;
   };
 
   // What to do with the tag ?
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/Homogeneous_base.h b/Homogeneous_kernel/include/CGAL/Homogeneous/Homogeneous_base.h
index b59b17e8255..12807f1fcc7 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/Homogeneous_base.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/Homogeneous_base.h
@@ -109,8 +109,13 @@ struct Homogeneous_base
                                                     Angle;
 
     template <typename T>
-    struct Dimension {
-      static const int value = T::static_dimension;
+    struct Ambiant_dimension {
+      typedef typename T::Ambiant_dimension type;
+    };
+
+    template <typename T>
+    struct Feature_dimension {
+      typedef typename T::Feature_dimension type;
     };
 
     typedef PointH2<Kernel>                         Point_2;
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Ambiant_dimension.tex b/Kernel_23/doc_tex/Kernel_23_ref/Ambiant_dimension.tex
new file mode 100644
index 00000000000..649a04b1d5b
--- /dev/null
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Ambiant_dimension.tex
@@ -0,0 +1,39 @@
+\begin{ccRefClass} {Ambiant_dimension<T, K = Kernel_traits<T>::Kernel>}
+
+\ccDefinition
+The class \ccRefName\ allows to retrieve the dimension of the ambiant space of
+a type.
+
+\ccInclude{CGAL/Dimension.h}
+
+\ccConstants
+
+\ccVariable{static const int value;}{The dimension value as a compile-time
+integral constant. It is implemented as \ccc{K::Dimension<T>::type::value}.
+It exists only when the dimension is a compile-time constant.}
+
+\ccTypes
+
+\ccTypedef{type;}{Either \ccc{Dimension_tag<dim>} if the dimension is a
+compile-time constant of value \ccc{dim}, or \ccc{Dynamic_dimension_tag}
+otherwise.  It is implemented as \ccc{K::Ambiant_dimension<T>::type}. }
+
+\ccCreation
+\ccCreationVariable{d}
+
+\ccExample
+
+The following retrieves the dimension of a point type.
+
+\begin{cprog}
+  typedef K::Point_2 Point;
+  int dimension = Ambiant_dimension<Point, K>::value;
+  assert(dimension == 2);
+\end{cprog} 
+
+\ccSeeAlso
+\ccRefConceptPage{Dimension_tag}
+\ccRefConceptPage{Dynamic_dimension_tag}
+\ccRefConceptPage{Feature_dimension}
+
+\end{ccRefClass} 
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Dimension.tex b/Kernel_23/doc_tex/Kernel_23_ref/Dimension.tex
deleted file mode 100644
index bdd1def1bdd..00000000000
--- a/Kernel_23/doc_tex/Kernel_23_ref/Dimension.tex
+++ /dev/null
@@ -1,31 +0,0 @@
-\begin{ccRefClass} {Dimension<T, K = Kernel_traits<T>::Kernel>}
-
-\ccDefinition
-The class \ccRefName\ allows to retrieve the dimension of the ambiant space of
-a type.  The dimension can also be the special constant
-\ccc{Dynamic_dimension}, which value is \ccc{INT_MAX}, to indicate the case
-where the dimension is only known at run time.
-
-\ccInclude{CGAL/Dimension.h}
-
-\ccConstants
-
-\ccVariable{static const int value;}{ The dimension. It is implemented as \ccc{K::Dimension<T>::value}. }
-
-\ccCreation
-\ccCreationVariable{d}
-
-\ccExample
-
-The following retrieves the dimension of a point type.
-
-\begin{cprog}
-  typedef Point_2<K> Point;
-  int dimension = Dimension<Point, K>::value;
-  assert(dimension == 2);
-\end{cprog} 
-
-\ccSeeAlso
-\ccRefConceptPage{Dimension_tag}
-
-\end{ccRefClass} 
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Dimension_tag.tex b/Kernel_23/doc_tex/Kernel_23_ref/Dimension_tag.tex
index 28f2c651ef2..41d9be00fcd 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Dimension_tag.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Dimension_tag.tex
@@ -6,7 +6,7 @@ for dispatching functions based on the dimension of an object, as provided
 by the \ccc{dim} parameter.  It is useful in cases where it is not more
 practical to pass the dimension as a template parameter directly.
 
-\ccInclude{CGAL/Dimension_tag.h}
+\ccInclude{CGAL/Dimension.h}
 
 \ccConstants
 
@@ -17,16 +17,19 @@ practical to pass the dimension as a template parameter directly.
 
 \ccExample
 
-The following declaration creates two points at the origin, either in 2D or in 3D.
+The following code declares two functions constructing two points at the origin,
+either in 2D or in 3D.
 
 \begin{cprog}
   Point_2<K> get_origin(Dimension_tag<2>) { return Point_2<K>(ORIGIN); }
   Point_3<K> get_origin(Dimension_tag<3>) { return Point_3<K>(ORIGIN); }
 
   std::cout << get_origin(Dimension_tag<2>())) << std::endl;
-\end{cprog} 
+\end{cprog}
 
 \ccSeeAlso
-\ccRefConceptPage{Dimension}
+\ccRefConceptPage{Ambiant_dimension}
+\ccRefConceptPage{Feature_dimension}
+\ccRefConceptPage{Dynamic_dimension_tag}
 
-\end{ccRefClass} 
+\end{ccRefClass}
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Dynamic_dimension_tag.tex b/Kernel_23/doc_tex/Kernel_23_ref/Dynamic_dimension_tag.tex
new file mode 100644
index 00000000000..17af60a4e33
--- /dev/null
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Dynamic_dimension_tag.tex
@@ -0,0 +1,32 @@
+\begin{ccRefClass} {Dynamic_dimension_tag}
+
+\ccDefinition
+An object of the class \ccRefName\ is an empty object which can be used
+for dispatching functions based on the dimension of an object.
+\ccRefName\ indicates that the dimension is not known at compile-time.
+\ccc{Dimension_tag} is the tag class dealing with compile-time dimensions.
+
+\ccInclude{CGAL/Dimension.h}
+
+\ccCreation
+\ccCreationVariable{d}
+
+\ccExample
+
+The following code declares two functions constructing two points at the origin,
+either in 2D or in 3D.
+
+\begin{cprog}
+  Point_2<K> get_origin(Dimension_tag<2>) { return Point_2<K>(ORIGIN); }
+  Point_3<K> get_origin(Dimension_tag<3>) { return Point_3<K>(ORIGIN); }
+  Point_d<K> get_origin(Dynamic_dmension_tag) { return Point_d<K>(ORIGIN); }
+
+  std::cout << get_origin(Dynamic_dimension_tag())) << std::endl;
+\end{cprog}
+
+\ccSeeAlso
+\ccRefConceptPage{Dimension_tag}
+\ccRefConceptPage{Ambiant_dimension}
+\ccRefConceptPage{Feature_dimension}
+
+\end{ccRefClass}
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Feature_dimension.tex b/Kernel_23/doc_tex/Kernel_23_ref/Feature_dimension.tex
new file mode 100644
index 00000000000..521961ee11a
--- /dev/null
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Feature_dimension.tex
@@ -0,0 +1,38 @@
+\begin{ccRefClass} {Feature_dimension<T, K = Kernel_traits<T>::Kernel>}
+
+\ccDefinition
+The class \ccRefName\ allows to retrieve the geometric dimension of a type.
+
+\ccInclude{CGAL/Dimension.h}
+
+\ccConstants
+
+\ccVariable{static const int value;}{The dimension value as a compile-time
+integral constant. It is implemented as \ccc{K::Feature_dimension<T>::type::value}.
+It exists only when the dimension is a compile-time constant.}
+
+\ccTypes
+
+\ccTypedef{type;}{Either \ccc{Dimension_tag<dim>} if the dimension is a
+compile-time constant of value \ccc{dim}, or \ccc{Dynamic_dimension_tag}
+otherwise.  It is implemented as \ccc{K::Feature_dimension<T>::type}. }
+
+\ccCreation
+\ccCreationVariable{d}
+
+\ccExample
+
+The following retrieves the dimension of a point type.
+
+\begin{cprog}
+  typedef K::Point_2 Point;
+  int dimension = Feature_dimension<Point, K>::value;
+  assert(dimension == 0);
+\end{cprog} 
+
+\ccSeeAlso
+\ccRefConceptPage{Dimension_tag}
+\ccRefConceptPage{Dynamic_dimension_tag}
+\ccRefConceptPage{Ambiant_dimension}
+
+\end{ccRefClass} 
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/main.tex b/Kernel_23/doc_tex/Kernel_23_ref/main.tex
index 1558b5e92cb..bdcc56b1520 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/main.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/main.tex
@@ -464,6 +464,8 @@ in the kernel.
 \section{Dimension handling tools}
 \gdef\ccRefPageBreak{\ccFalse}
 
-\input{Kernel_23_ref/Dimension.tex}
+\input{Kernel_23_ref/Ambiant_dimension.tex}
+\input{Kernel_23_ref/Feature_dimension.tex}
 \gdef\ccRefPageBreak{\ccTrue}
 \input{Kernel_23_ref/Dimension_tag.tex}
+\input{Kernel_23_ref/Dynamic_dimension_tag.tex}
diff --git a/Kernel_23/include/CGAL/Aff_transformation_2.h b/Kernel_23/include/CGAL/Aff_transformation_2.h
index 124cf274373..249fc4b60de 100644
--- a/Kernel_23/include/CGAL/Aff_transformation_2.h
+++ b/Kernel_23/include/CGAL/Aff_transformation_2.h
@@ -18,14 +18,13 @@
 // $URL$
 // $Id$
 // 
-//
-// Author(s)     : Andreas Fabri
-//                 Stefan Schirra
+// Author(s)     : Andreas Fabri, Stefan Schirra
 
 #ifndef CGAL_AFF_TRANSFORMATION_2_H
 #define CGAL_AFF_TRANSFORMATION_2_H
 
 #include <CGAL/basic.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -39,9 +38,10 @@ class Aff_transformation_2 : public R_::Kernel_base::Aff_transformation_2
   typedef typename R_::Vector_2              Vector_2;
   typedef typename R_::Kernel_base::Aff_transformation_2 RAff_transformation_2;
 public:
-  typedef  R_                               R;
 
-  static const int static_dimension = 2;
+  typedef CGAL::Dimension_tag<2>            Ambiant_dimension;
+
+  typedef  R_                               R;
 
   Aff_transformation_2() {}
 
diff --git a/Kernel_23/include/CGAL/Aff_transformation_3.h b/Kernel_23/include/CGAL/Aff_transformation_3.h
index 4d2cbe3ba24..00e22f25744 100644
--- a/Kernel_23/include/CGAL/Aff_transformation_3.h
+++ b/Kernel_23/include/CGAL/Aff_transformation_3.h
@@ -17,13 +17,14 @@
 //
 // $URL$
 // $Id$
-// 
 //
 // Author(s)     : Andreas Fabri, Stefan Schirra
 
 #ifndef CGAL_AFF_TRANSFORMATION_3_H
 #define CGAL_AFF_TRANSFORMATION_3_H
 
+#include <CGAL/Dimension.h>
+
 CGAL_BEGIN_NAMESPACE
 
 template <class R_>
@@ -34,7 +35,7 @@ class Aff_transformation_3 : public R_::Kernel_base::Aff_transformation_3
   typedef typename R_::Kernel_base::Aff_transformation_3 RAff_transformation_3;
 public:
 
-  static const int static_dimension = 3;
+  typedef CGAL::Dimension_tag<3>    Ambiant_dimension;
 
   typedef R_                        R;
 
diff --git a/Kernel_23/include/CGAL/Bbox_2.h b/Kernel_23/include/CGAL/Bbox_2.h
index 6242d6367b0..7a610db6492 100644
--- a/Kernel_23/include/CGAL/Bbox_2.h
+++ b/Kernel_23/include/CGAL/Bbox_2.h
@@ -18,7 +18,6 @@
 // $URL$
 // $Id$
 //
-//
 // Author(s)     : Andreas Fabri
 
 #ifndef CGAL_BBOX_2_H
@@ -28,9 +27,13 @@
 #include <CGAL/kernel_assertions.h>
 #include <CGAL/IO/io.h>
 #include <CGAL/Fourtuple.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
+template < typename T >
+struct Simple_cartesian;
+
 class Bbox_2
 {
   typedef Fourtuple<double>            BBox_rep_2;
@@ -39,7 +42,10 @@ class Bbox_2
 
 public:
 
-  static const int static_dimension = 2;
+  typedef Dimension_tag<2>  Ambiant_dimension;
+  typedef Dimension_tag<2>  Feature_dimension;
+
+  typedef Simple_cartesian<double>  R;
 
              Bbox_2() {}
 
diff --git a/Kernel_23/include/CGAL/Bbox_3.h b/Kernel_23/include/CGAL/Bbox_3.h
index 2267d23df76..fbdf4f5f29d 100644
--- a/Kernel_23/include/CGAL/Bbox_3.h
+++ b/Kernel_23/include/CGAL/Bbox_3.h
@@ -18,7 +18,6 @@
 // $URL$
 // $Id$
 //
-//
 // Author(s)     : Andreas Fabri
 
 #ifndef CGAL_BBOX_3_H
@@ -27,16 +26,23 @@
 #include <CGAL/basic.h>
 #include <CGAL/IO/io.h>
 #include <CGAL/Sixtuple.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
+template < typename T >
+struct Simple_cartesian;
+
 class Bbox_3
 {
   Sixtuple<double>   rep;
 
 public:
 
-  static const int static_dimension = 3;
+  typedef Dimension_tag<3>  Ambiant_dimension;
+  typedef Dimension_tag<3>  Feature_dimension;
+
+  typedef Simple_cartesian<double>  R;
 
         Bbox_3() {}
 
diff --git a/Kernel_23/include/CGAL/Circle_2.h b/Kernel_23/include/CGAL/Circle_2.h
index bd9426285fd..8ab24c6ac1c 100644
--- a/Kernel_23/include/CGAL/Circle_2.h
+++ b/Kernel_23/include/CGAL/Circle_2.h
@@ -29,6 +29,7 @@
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/Bbox_2.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -45,7 +46,8 @@ class Circle_2 : public R_::Kernel_base::Circle_2
 
 public:
 
-  static const int static_dimension = 2;
+  typedef Dimension_tag<2>  Ambiant_dimension;
+  typedef Dimension_tag<1>  Feature_dimension;
 
   typedef RCircle_2 Rep;
 
diff --git a/Kernel_23/include/CGAL/Dimension.h b/Kernel_23/include/CGAL/Dimension.h
index 3a42e631884..eec299299cc 100644
--- a/Kernel_23/include/CGAL/Dimension.h
+++ b/Kernel_23/include/CGAL/Dimension.h
@@ -1,8 +1,5 @@
-// Copyright (c) 2005  Utrecht University (The Netherlands),
-// ETH Zurich (Switzerland), Freie Universitaet Berlin (Germany),
-// INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg
-// (Germany), Max-Planck-Institute Saarbruecken (Germany), RISC Linz (Austria),
-// and Tel-Aviv University (Israel).  All rights reserved.
+// Copyright (c) 2008  INRIA Sophia-Antipolis (France).
+// Aviv University (Israel).  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 Lesser General Public License as
@@ -17,7 +14,6 @@
 //
 // $URL$
 // $Id$
-// 
 //
 // Author(s)     : Sylvain Pion
 
@@ -30,16 +26,48 @@
 
 CGAL_BEGIN_NAMESPACE
 
-// This is a tool to obtain the static dimension of a kernel object.
-// That is, the dimension of the ambiant space.
+// These tag classes help dispatching functions based on a geometric dimension.
 
-template < typename T, typename K = typename Kernel_traits<T>::Kernel >
-struct Dimension
+template < int dim >
+struct Dimension_tag
 {
-  static const int value = K::template Dimension<T>::value;
+  static const int value = dim;
 };
 
-static const int Dynamic_dimension = INT_MAX;
+struct Dynamic_dimension_tag {};
+
+
+namespace CGALi {
+
+  template < typename D >
+  struct Dim_value {
+    static const int value = D::value;
+  };
+
+  template <>
+  struct Dim_value <Dynamic_dimension_tag> {};
+
+} // namespace CGALi
+
+
+// Ambiant_dimension gives access to the dimension of the ambiant space of an object.
+
+template < typename T, typename K = typename Kernel_traits<T>::Kernel >
+struct Ambiant_dimension
+  : public CGALi::Dim_value< typename K::template Ambiant_dimension<T>::type >
+{
+  typedef typename K::template Ambiant_dimension<T>::type type;
+};
+
+
+// Feature_dimension gives access to the dimension of an object.
+
+template < typename T, typename K = typename Kernel_traits<T>::Kernel >
+struct Feature_dimension
+  : public CGALi::Dim_value< typename K::template Feature_dimension<T>::type >
+{
+  typedef typename K::template Feature_dimension<T>::type type;
+};
 
 CGAL_END_NAMESPACE
 
diff --git a/Kernel_23/include/CGAL/Dimension_tag.h b/Kernel_23/include/CGAL/Dimension_tag.h
deleted file mode 100644
index aa1632ae2ef..00000000000
--- a/Kernel_23/include/CGAL/Dimension_tag.h
+++ /dev/null
@@ -1,37 +0,0 @@
-// Copyright (c) 2008  INRIA Sophia-Antipolis (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 Lesser General Public License as
-// published by the Free Software Foundation; version 2.1 of the License.
-// See the file LICENSE.LGPL distributed with CGAL.
-//
-// 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)     : Sylvain Pion
-
-#ifndef CGAL_DIMENSION_TAG_H
-#define CGAL_DIMENSION_TAG_H
-
-#include <CGAL/basic.h>
-
-CGAL_BEGIN_NAMESPACE
-
-// This class helps dispatching functions based on the geometric dimension.
-
-template < int dim >
-struct Dimension_tag
-{
-  static const int value = dim;
-};
-
-CGAL_END_NAMESPACE
-
-#endif // CGAL_DIMENSION_TAG_H
diff --git a/Kernel_23/include/CGAL/Direction_2.h b/Kernel_23/include/CGAL/Direction_2.h
index c70b5df99cf..a008ba765b2 100644
--- a/Kernel_23/include/CGAL/Direction_2.h
+++ b/Kernel_23/include/CGAL/Direction_2.h
@@ -28,6 +28,7 @@
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/representation_tags.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -47,7 +48,8 @@ class Direction_2 : public R_::Kernel_base::Direction_2
 
 public:
 
-  static const int static_dimension = 2;
+  typedef Dimension_tag<2>  Ambiant_dimension;
+  typedef Dimension_tag<0>  Feature_dimension;
 
   typedef RDirection_2 Rep;
 
diff --git a/Kernel_23/include/CGAL/Direction_3.h b/Kernel_23/include/CGAL/Direction_3.h
index 7eefaf7ac5d..ebb203cbc06 100644
--- a/Kernel_23/include/CGAL/Direction_3.h
+++ b/Kernel_23/include/CGAL/Direction_3.h
@@ -28,6 +28,7 @@
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/representation_tags.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -46,7 +47,8 @@ class Direction_3 : public R_::Kernel_base::Direction_3
 
 public:
 
-  static const int static_dimension = 3;
+  typedef Dimension_tag<3>  Ambiant_dimension;
+  typedef Dimension_tag<0>  Feature_dimension;
 
   typedef typename R_::Kernel_base::Direction_3 Rep;
 
diff --git a/Kernel_23/include/CGAL/Iso_cuboid_3.h b/Kernel_23/include/CGAL/Iso_cuboid_3.h
index 5d7e2b96689..305ece6f8f3 100644
--- a/Kernel_23/include/CGAL/Iso_cuboid_3.h
+++ b/Kernel_23/include/CGAL/Iso_cuboid_3.h
@@ -28,6 +28,7 @@
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/Bbox_3.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -43,7 +44,8 @@ class Iso_cuboid_3 : public R_::Kernel_base::Iso_cuboid_3
 
 public:
 
-  static const int static_dimension = 3;
+  typedef Dimension_tag<3>  Ambiant_dimension;
+  typedef Dimension_tag<3>  Feature_dimension;
 
   typedef typename R_::Kernel_base::Iso_cuboid_3  Rep;
 
diff --git a/Kernel_23/include/CGAL/Iso_rectangle_2.h b/Kernel_23/include/CGAL/Iso_rectangle_2.h
index 400f20a075c..11cd16aa71a 100644
--- a/Kernel_23/include/CGAL/Iso_rectangle_2.h
+++ b/Kernel_23/include/CGAL/Iso_rectangle_2.h
@@ -28,6 +28,7 @@
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/Bbox_2.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -44,7 +45,8 @@ class Iso_rectangle_2 : public R_::Kernel_base::Iso_rectangle_2
 
 public:
 
-  static const int static_dimension = 2;
+  typedef Dimension_tag<2>  Ambiant_dimension;
+  typedef Dimension_tag<2>  Feature_dimension;
 
   typedef typename R_::Kernel_base::Iso_rectangle_2  Rep;
 
diff --git a/Kernel_23/include/CGAL/Line_2.h b/Kernel_23/include/CGAL/Line_2.h
index 20f388d8d0d..88e828035f9 100644
--- a/Kernel_23/include/CGAL/Line_2.h
+++ b/Kernel_23/include/CGAL/Line_2.h
@@ -27,6 +27,7 @@
 #include <boost/static_assert.hpp>
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -48,7 +49,8 @@ class Line_2 : public R_::Kernel_base::Line_2
 
 public:
 
-  static const int static_dimension = 2;
+  typedef Dimension_tag<2>  Ambiant_dimension;
+  typedef Dimension_tag<1>  Feature_dimension;
 
   typedef RLine_2 Rep;
 
diff --git a/Kernel_23/include/CGAL/Line_3.h b/Kernel_23/include/CGAL/Line_3.h
index 5adba15ccba..0a9e4277a65 100644
--- a/Kernel_23/include/CGAL/Line_3.h
+++ b/Kernel_23/include/CGAL/Line_3.h
@@ -28,6 +28,7 @@
 #include <boost/static_assert.hpp>
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -48,7 +49,8 @@ class Line_3 : public R_::Kernel_base::Line_3
 
 public:
 
-  static const int static_dimension = 3;
+  typedef Dimension_tag<3>  Ambiant_dimension;
+  typedef Dimension_tag<1>  Feature_dimension;
 
   typedef typename R_::Kernel_base::Line_3   Rep;
 
diff --git a/Kernel_23/include/CGAL/Plane_3.h b/Kernel_23/include/CGAL/Plane_3.h
index ec095fa0e3e..e07c50b55b2 100644
--- a/Kernel_23/include/CGAL/Plane_3.h
+++ b/Kernel_23/include/CGAL/Plane_3.h
@@ -27,6 +27,7 @@
 #include <boost/static_assert.hpp>
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -48,7 +49,8 @@ class Plane_3 : public R_::Kernel_base::Plane_3
 
 public:
 
-  static const int static_dimension = 3;
+  typedef Dimension_tag<3>  Ambiant_dimension;
+  typedef Dimension_tag<2>  Feature_dimension;
 
   typedef typename R_::Kernel_base::Plane_3  Rep;
 
diff --git a/Kernel_23/include/CGAL/Point_2.h b/Kernel_23/include/CGAL/Point_2.h
index 46ad95e3945..99afa28758e 100644
--- a/Kernel_23/include/CGAL/Point_2.h
+++ b/Kernel_23/include/CGAL/Point_2.h
@@ -30,6 +30,7 @@
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/representation_tags.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -47,7 +48,8 @@ class Point_2 : public R_::Kernel_base::Point_2
 
 public:
 
-  static const int static_dimension = 2;
+  typedef Dimension_tag<2>  Ambiant_dimension;
+  typedef Dimension_tag<0>  Feature_dimension;
 
   typedef RPoint_2 Rep;
   typedef typename R_::Cartesian_const_iterator_2 Cartesian_const_iterator;
diff --git a/Kernel_23/include/CGAL/Point_3.h b/Kernel_23/include/CGAL/Point_3.h
index 71aa0e927da..8e02600a6fb 100644
--- a/Kernel_23/include/CGAL/Point_3.h
+++ b/Kernel_23/include/CGAL/Point_3.h
@@ -31,6 +31,7 @@
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/Bbox_3.h>
 #include <CGAL/representation_tags.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -47,7 +48,8 @@ class Point_3 : public R_::Kernel_base::Point_3
 
 public:
 
-  static const int static_dimension = 3;
+  typedef Dimension_tag<3>  Ambiant_dimension;
+  typedef Dimension_tag<0>  Feature_dimension;
 
   typedef typename R_::Kernel_base::Point_3  Rep;
   typedef typename R_::Cartesian_const_iterator_3 Cartesian_const_iterator;
diff --git a/Kernel_23/include/CGAL/Ray_2.h b/Kernel_23/include/CGAL/Ray_2.h
index 5b5eaa7f53e..6bb4d233f85 100644
--- a/Kernel_23/include/CGAL/Ray_2.h
+++ b/Kernel_23/include/CGAL/Ray_2.h
@@ -28,6 +28,7 @@
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/representation_tags.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -49,7 +50,8 @@ class Ray_2 : public R_::Kernel_base::Ray_2
 
 public:
 
-  static const int static_dimension = 2;
+  typedef Dimension_tag<2>  Ambiant_dimension;
+  typedef Dimension_tag<1>  Feature_dimension;
 
   typedef RRay_2 Rep;
 
diff --git a/Kernel_23/include/CGAL/Ray_3.h b/Kernel_23/include/CGAL/Ray_3.h
index beb41b3cf42..d3138680ca3 100644
--- a/Kernel_23/include/CGAL/Ray_3.h
+++ b/Kernel_23/include/CGAL/Ray_3.h
@@ -28,6 +28,7 @@
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/representation_tags.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -46,7 +47,8 @@ class Ray_3 : public R_::Kernel_base::Ray_3
 
 public:
 
-  static const int static_dimension = 3;
+  typedef Dimension_tag<3>  Ambiant_dimension;
+  typedef Dimension_tag<1>  Feature_dimension;
 
   typedef typename R_::Kernel_base::Ray_3    Rep;
 
diff --git a/Kernel_23/include/CGAL/Segment_2.h b/Kernel_23/include/CGAL/Segment_2.h
index d023e36cb23..f3614ff119f 100644
--- a/Kernel_23/include/CGAL/Segment_2.h
+++ b/Kernel_23/include/CGAL/Segment_2.h
@@ -28,6 +28,7 @@
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/Bbox_2.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -48,7 +49,8 @@ class Segment_2 : public R_::Kernel_base::Segment_2
 
 public:
 
-  static const int static_dimension = 2;
+  typedef Dimension_tag<2>  Ambiant_dimension;
+  typedef Dimension_tag<1>  Feature_dimension;
 
   typedef RSegment_2 Rep;
 
diff --git a/Kernel_23/include/CGAL/Segment_3.h b/Kernel_23/include/CGAL/Segment_3.h
index fd23a6708cf..d1abf85b1b5 100644
--- a/Kernel_23/include/CGAL/Segment_3.h
+++ b/Kernel_23/include/CGAL/Segment_3.h
@@ -28,6 +28,7 @@
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/Bbox_3.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -47,7 +48,8 @@ class Segment_3 : public R_::Kernel_base::Segment_3
 
 public:
 
-  static const int static_dimension = 3;
+  typedef Dimension_tag<3>  Ambiant_dimension;
+  typedef Dimension_tag<1>  Feature_dimension;
 
   typedef typename R_::Kernel_base::Segment_3  Rep;
 
diff --git a/Kernel_23/include/CGAL/Sphere_3.h b/Kernel_23/include/CGAL/Sphere_3.h
index e730c6bb66a..77521680eb3 100644
--- a/Kernel_23/include/CGAL/Sphere_3.h
+++ b/Kernel_23/include/CGAL/Sphere_3.h
@@ -29,6 +29,7 @@
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/Bbox_3.h>
 #include <CGAL/representation_tags.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -44,7 +45,8 @@ class Sphere_3 : public R_::Kernel_base::Sphere_3
 
 public:
 
-  static const int static_dimension = 3;
+  typedef Dimension_tag<3>  Ambiant_dimension;
+  typedef Dimension_tag<2>  Feature_dimension;
 
   typedef typename R_::Kernel_base::Sphere_3  Rep;
 
diff --git a/Kernel_23/include/CGAL/Tetrahedron_3.h b/Kernel_23/include/CGAL/Tetrahedron_3.h
index a31a3a57976..99d62f41262 100644
--- a/Kernel_23/include/CGAL/Tetrahedron_3.h
+++ b/Kernel_23/include/CGAL/Tetrahedron_3.h
@@ -28,6 +28,7 @@
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/Bbox_3.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -42,7 +43,8 @@ class Tetrahedron_3 : public R_::Kernel_base::Tetrahedron_3
 
 public:
 
-  static const int static_dimension = 3;
+  typedef Dimension_tag<3>  Ambiant_dimension;
+  typedef Dimension_tag<3>  Feature_dimension;
 
   typedef typename R_::Kernel_base::Tetrahedron_3  Rep;
 
diff --git a/Kernel_23/include/CGAL/Triangle_2.h b/Kernel_23/include/CGAL/Triangle_2.h
index c22c4770fd5..0244dd67a6f 100644
--- a/Kernel_23/include/CGAL/Triangle_2.h
+++ b/Kernel_23/include/CGAL/Triangle_2.h
@@ -28,6 +28,7 @@
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/Bbox_2.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -43,7 +44,8 @@ class Triangle_2 : public R_::Kernel_base::Triangle_2
 
 public:
 
-  static const int static_dimension = 2;
+  typedef Dimension_tag<2>  Ambiant_dimension;
+  typedef Dimension_tag<2>  Feature_dimension;
 
   typedef RTriangle_2 Rep;
 
diff --git a/Kernel_23/include/CGAL/Triangle_3.h b/Kernel_23/include/CGAL/Triangle_3.h
index 665e7f8e12c..5cda52364f1 100644
--- a/Kernel_23/include/CGAL/Triangle_3.h
+++ b/Kernel_23/include/CGAL/Triangle_3.h
@@ -28,6 +28,7 @@
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/Bbox_3.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -45,7 +46,8 @@ class Triangle_3 : public R_::Kernel_base::Triangle_3
 
 public:
 
-  static const int static_dimension = 3;
+  typedef Dimension_tag<3>  Ambiant_dimension;
+  typedef Dimension_tag<2>  Feature_dimension;
 
   typedef typename R_::Kernel_base::Triangle_3  Rep;
 
diff --git a/Kernel_23/include/CGAL/Vector_2.h b/Kernel_23/include/CGAL/Vector_2.h
index 36839d88da6..33adf82d275 100644
--- a/Kernel_23/include/CGAL/Vector_2.h
+++ b/Kernel_23/include/CGAL/Vector_2.h
@@ -30,6 +30,7 @@
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/representation_tags.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -51,7 +52,8 @@ class Vector_2 : public R_::Kernel_base::Vector_2
 
 public:
 
-  static const int static_dimension = 2;
+  typedef Dimension_tag<2>  Ambiant_dimension;
+  typedef Dimension_tag<0>  Feature_dimension;
 
   typedef RVector_2 Rep;
   typedef typename R_::Cartesian_const_iterator_2 Cartesian_const_iterator;
diff --git a/Kernel_23/include/CGAL/Vector_3.h b/Kernel_23/include/CGAL/Vector_3.h
index bb77390c23d..800d712cf18 100644
--- a/Kernel_23/include/CGAL/Vector_3.h
+++ b/Kernel_23/include/CGAL/Vector_3.h
@@ -30,6 +30,7 @@
 #include <boost/static_assert.hpp>
 #include <boost/type_traits.hpp>
 #include <CGAL/Kernel/Return_base_tag.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -50,7 +51,8 @@ class Vector_3 : public R_::Kernel_base::Vector_3
 
 public:
 
-  static const int static_dimension = 3;
+  typedef Dimension_tag<3>  Ambiant_dimension;
+  typedef Dimension_tag<0>  Feature_dimension;
 
   typedef typename R_::Cartesian_const_iterator_3 Cartesian_const_iterator;
   typedef typename R_::Kernel_base::Vector_3      Rep;
diff --git a/Kernel_23/test/Kernel_23/Dimension.cpp b/Kernel_23/test/Kernel_23/Dimension.cpp
index 1e450a38341..8fde9e20ef3 100644
--- a/Kernel_23/test/Kernel_23/Dimension.cpp
+++ b/Kernel_23/test/Kernel_23/Dimension.cpp
@@ -1,5 +1,5 @@
-// Test program for Dimension<>.
-// Sylvain Pion, 2005.
+// Test program for Ambiant_dimension<> and Feature_dimension<>.
+// Sylvain Pion, 2005, 2008.
 
 #include <cassert>
 #include <CGAL/Cartesian.h>
@@ -10,65 +10,107 @@
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
 
 #include <CGAL/Dimension.h>
-#include <CGAL/Dimension_tag.h>
+#include <CGAL/Dimension.h>
 
 template < typename K >
 void test(CGAL::Dimension_tag<2>)
 {
-  assert( 2 == CGAL::Dimension<typename K::Point_2>::value );
-  assert( 2 == CGAL::Dimension<typename K::Vector_2>::value );
-  assert( 2 == CGAL::Dimension<typename K::Direction_2>::value );
-  assert( 2 == CGAL::Dimension<typename K::Line_2>::value );
-  assert( 2 == CGAL::Dimension<typename K::Ray_2>::value );
-  assert( 2 == CGAL::Dimension<typename K::Segment_2>::value );
-  assert( 2 == CGAL::Dimension<typename K::Triangle_2>::value );
-  assert( 2 == CGAL::Dimension<typename K::Iso_rectangle_2>::value );
-  assert( 2 == CGAL::Dimension<typename K::Circle_2>::value );
-  assert( 2 == CGAL::Dimension<typename K::Conic_2>::value );
-  assert( 2 == CGAL::Dimension<typename K::Aff_transformation_2>::value );
+  assert( 2 == CGAL::Ambiant_dimension<typename K::Point_2>::value );
+  assert( 2 == CGAL::Ambiant_dimension<typename K::Vector_2>::value );
+  assert( 2 == CGAL::Ambiant_dimension<typename K::Direction_2>::value );
+  assert( 2 == CGAL::Ambiant_dimension<typename K::Line_2>::value );
+  assert( 2 == CGAL::Ambiant_dimension<typename K::Ray_2>::value );
+  assert( 2 == CGAL::Ambiant_dimension<typename K::Segment_2>::value );
+  assert( 2 == CGAL::Ambiant_dimension<typename K::Triangle_2>::value );
+  assert( 2 == CGAL::Ambiant_dimension<typename K::Iso_rectangle_2>::value );
+  assert( 2 == CGAL::Ambiant_dimension<typename K::Circle_2>::value );
+  assert( 2 == CGAL::Ambiant_dimension<typename K::Conic_2>::value );
+  assert( 2 == CGAL::Ambiant_dimension<typename K::Aff_transformation_2>::value );
+  assert( 2 == CGAL::Ambiant_dimension<CGAL::Bbox_2>::value );
+
+  assert( 0 == CGAL::Feature_dimension<typename K::Point_2>::value );
+  assert( 0 == CGAL::Feature_dimension<typename K::Vector_2>::value );
+  assert( 0 == CGAL::Feature_dimension<typename K::Direction_2>::value );
+  assert( 1 == CGAL::Feature_dimension<typename K::Line_2>::value );
+  assert( 1 == CGAL::Feature_dimension<typename K::Ray_2>::value );
+  assert( 1 == CGAL::Feature_dimension<typename K::Segment_2>::value );
+  assert( 2 == CGAL::Feature_dimension<typename K::Triangle_2>::value );
+  assert( 2 == CGAL::Feature_dimension<typename K::Iso_rectangle_2>::value );
+  assert( 1 == CGAL::Feature_dimension<typename K::Circle_2>::value );
+  assert( 1 == CGAL::Feature_dimension<typename K::Conic_2>::value );
+  // assert( ? == CGAL::Feature_dimension<typename K::Aff_transformation_2>::value );
+  assert( 2 == CGAL::Feature_dimension<CGAL::Bbox_2>::value );
 }
 
 template < typename K >
 void test(CGAL::Dimension_tag<3>)
 {
-  assert( 3 == CGAL::Dimension<typename K::Point_3>::value );
-  assert( 3 == CGAL::Dimension<typename K::Plane_3>::value );
-  assert( 3 == CGAL::Dimension<typename K::Vector_3>::value );
-  assert( 3 == CGAL::Dimension<typename K::Direction_3>::value );
-  assert( 3 == CGAL::Dimension<typename K::Line_3>::value );
-  assert( 3 == CGAL::Dimension<typename K::Ray_3>::value );
-  assert( 3 == CGAL::Dimension<typename K::Segment_3>::value );
-  assert( 3 == CGAL::Dimension<typename K::Triangle_3>::value );
-  assert( 3 == CGAL::Dimension<typename K::Tetrahedron_3>::value );
-  assert( 3 == CGAL::Dimension<typename K::Iso_cuboid_3>::value );
-  assert( 3 == CGAL::Dimension<typename K::Sphere_3>::value );
-  assert( 3 == CGAL::Dimension<typename K::Aff_transformation_3>::value );
+  assert( 3 == CGAL::Ambiant_dimension<typename K::Point_3>::value );
+  assert( 3 == CGAL::Ambiant_dimension<typename K::Plane_3>::value );
+  assert( 3 == CGAL::Ambiant_dimension<typename K::Vector_3>::value );
+  assert( 3 == CGAL::Ambiant_dimension<typename K::Direction_3>::value );
+  assert( 3 == CGAL::Ambiant_dimension<typename K::Line_3>::value );
+  assert( 3 == CGAL::Ambiant_dimension<typename K::Ray_3>::value );
+  assert( 3 == CGAL::Ambiant_dimension<typename K::Segment_3>::value );
+  assert( 3 == CGAL::Ambiant_dimension<typename K::Triangle_3>::value );
+  assert( 3 == CGAL::Ambiant_dimension<typename K::Tetrahedron_3>::value );
+  assert( 3 == CGAL::Ambiant_dimension<typename K::Iso_cuboid_3>::value );
+  assert( 3 == CGAL::Ambiant_dimension<typename K::Sphere_3>::value );
+  assert( 3 == CGAL::Ambiant_dimension<typename K::Aff_transformation_3>::value );
+  assert( 3 == CGAL::Ambiant_dimension<CGAL::Bbox_3>::value );
+
+  assert( 0 == CGAL::Feature_dimension<typename K::Point_3>::value );
+  assert( 2 == CGAL::Feature_dimension<typename K::Plane_3>::value );
+  assert( 0 == CGAL::Feature_dimension<typename K::Vector_3>::value );
+  assert( 0 == CGAL::Feature_dimension<typename K::Direction_3>::value );
+  assert( 1 == CGAL::Feature_dimension<typename K::Line_3>::value );
+  assert( 1 == CGAL::Feature_dimension<typename K::Ray_3>::value );
+  assert( 1 == CGAL::Feature_dimension<typename K::Segment_3>::value );
+  assert( 2 == CGAL::Feature_dimension<typename K::Triangle_3>::value );
+  assert( 3 == CGAL::Feature_dimension<typename K::Tetrahedron_3>::value );
+  assert( 3 == CGAL::Feature_dimension<typename K::Iso_cuboid_3>::value );
+  assert( 2 == CGAL::Feature_dimension<typename K::Sphere_3>::value );
+  // assert( ? == CGAL::Feature_dimension<typename K::Aff_transformation_3>::value );
+  assert( 3 == CGAL::Feature_dimension<CGAL::Bbox_3>::value );
 }
 
+void check_dyn_dim(CGAL::Dynamic_dimension_tag) {}
+
 template < typename K >
-void test(CGAL::Dimension_tag<CGAL::Dynamic_dimension>)
+void test(CGAL::Dynamic_dimension_tag)
 {
-  assert( CGAL::Dynamic_dimension == CGAL::Dimension<typename K::Point_d>::value );
-  assert( CGAL::Dynamic_dimension == CGAL::Dimension<typename K::Hyperplane_d>::value );
-  assert( CGAL::Dynamic_dimension == CGAL::Dimension<typename K::Vector_d>::value );
-  assert( CGAL::Dynamic_dimension == CGAL::Dimension<typename K::Direction_d>::value );
-  assert( CGAL::Dynamic_dimension == CGAL::Dimension<typename K::Line_d>::value );
-  assert( CGAL::Dynamic_dimension == CGAL::Dimension<typename K::Ray_d>::value );
-  assert( CGAL::Dynamic_dimension == CGAL::Dimension<typename K::Segment_d>::value );
-  assert( CGAL::Dynamic_dimension == CGAL::Dimension<typename K::Iso_box_d>::value );
-  assert( CGAL::Dynamic_dimension == CGAL::Dimension<typename K::Sphere_d>::value );
-  assert( CGAL::Dynamic_dimension == CGAL::Dimension<typename K::Aff_transformation_d>::value );
+  check_dyn_dim(typename CGAL::Ambiant_dimension<typename K::Point_d>::type() );
+  check_dyn_dim(typename CGAL::Ambiant_dimension<typename K::Hyperplane_d>::type() );
+  check_dyn_dim(typename CGAL::Ambiant_dimension<typename K::Vector_d>::type() );
+  check_dyn_dim(typename CGAL::Ambiant_dimension<typename K::Direction_d>::type() );
+  check_dyn_dim(typename CGAL::Ambiant_dimension<typename K::Line_d>::type() );
+  check_dyn_dim(typename CGAL::Ambiant_dimension<typename K::Ray_d>::type() );
+  check_dyn_dim(typename CGAL::Ambiant_dimension<typename K::Segment_d>::type() );
+  check_dyn_dim(typename CGAL::Ambiant_dimension<typename K::Iso_box_d>::type() );
+  check_dyn_dim(typename CGAL::Ambiant_dimension<typename K::Sphere_d>::type() );
+  check_dyn_dim(typename CGAL::Ambiant_dimension<typename K::Aff_transformation_d>::type() );
+
+  assert( 0 == CGAL::Feature_dimension<typename K::Point_d>::value );
+  assert( 0 == CGAL::Feature_dimension<typename K::Vector_d>::value );
+  assert( 0 == CGAL::Feature_dimension<typename K::Direction_d>::value );
+  assert( 1 == CGAL::Feature_dimension<typename K::Line_d>::value );
+  assert( 1 == CGAL::Feature_dimension<typename K::Ray_d>::value );
+  assert( 1 == CGAL::Feature_dimension<typename K::Segment_d>::value );
+  check_dyn_dim(typename CGAL::Feature_dimension<typename K::Hyperplane_d>::type() );
+  check_dyn_dim(typename CGAL::Feature_dimension<typename K::Iso_box_d>::type() );
+  check_dyn_dim(typename CGAL::Feature_dimension<typename K::Sphere_d>::type() );
+  // check_dyn_dim(typename CGAL::Feature_dimension<typename K::Aff_transformation_d>::type() );
 }
 
 int main()
 {
   test<CGAL::Cartesian<int> >(CGAL::Dimension_tag<2>());
   test<CGAL::Cartesian<int> >(CGAL::Dimension_tag<3>());
-  test<CGAL::Cartesian_d<int> >(CGAL::Dimension_tag<CGAL::Dynamic_dimension>());
+  test<CGAL::Cartesian_d<int> >(CGAL::Dynamic_dimension_tag());
 
   test<CGAL::Homogeneous<int> >(CGAL::Dimension_tag<2>());
   test<CGAL::Homogeneous<int> >(CGAL::Dimension_tag<3>());
-  test<CGAL::Homogeneous_d<int> >(CGAL::Dimension_tag<CGAL::Dynamic_dimension>());
+  test<CGAL::Homogeneous_d<int> >(CGAL::Dynamic_dimension_tag());
   
   test<CGAL::Exact_predicates_inexact_constructions_kernel>(CGAL::Dimension_tag<2>());
   test<CGAL::Exact_predicates_inexact_constructions_kernel>(CGAL::Dimension_tag<3>());
diff --git a/Kernel_d/include/CGAL/Cartesian_d.h b/Kernel_d/include/CGAL/Cartesian_d.h
index 3edcc15c457..a79091eb81b 100644
--- a/Kernel_d/include/CGAL/Cartesian_d.h
+++ b/Kernel_d/include/CGAL/Cartesian_d.h
@@ -46,8 +46,6 @@
 #include <CGAL/Kernel_d/Interface_classes.h>
 #include <CGAL/Kernel_d/simple_objects.h>
 
-#include <CGAL/Dimension.h>
-
 CGAL_BEGIN_NAMESPACE
 
 template <class pFT, class pLA = Linear_algebraCd<pFT> >
@@ -76,9 +74,14 @@ public:
 
   typedef typename Point_d_base::Cartesian_const_iterator Cartesian_const_iterator_d;
 
-  template <typename>
-  struct Dimension {
-    static const int value = Dynamic_dimension;
+  template <typename T>
+  struct Ambiant_dimension {
+    typedef typename T::Ambiant_dimension type;
+  };
+
+  template <typename T>
+  struct Feature_dimension {
+    typedef typename T::Feature_dimension type;
   };
 
   template <typename K>
diff --git a/Kernel_d/include/CGAL/Homogeneous_d.h b/Kernel_d/include/CGAL/Homogeneous_d.h
index 0a8c51da83b..79f3607d09c 100644
--- a/Kernel_d/include/CGAL/Homogeneous_d.h
+++ b/Kernel_d/include/CGAL/Homogeneous_d.h
@@ -47,8 +47,6 @@
 #include <CGAL/Kernel_d/Interface_classes.h>
 #include <CGAL/Kernel_d/simple_objects.h>
 
-#include <CGAL/Dimension.h>
-
 CGAL_BEGIN_NAMESPACE
 
 template <class pRT, class pLA = Linear_algebraHd<pRT> >
@@ -76,9 +74,14 @@ public:
 
   typedef typename Point_d_base::Cartesian_const_iterator Cartesian_const_iterator_d;
 
-  template <typename>
-  struct Dimension {
-    static const int value = Dynamic_dimension;
+  template <typename T>
+  struct Ambiant_dimension {
+    typedef typename T::Ambiant_dimension type;
+  };
+
+  template <typename T>
+  struct Feature_dimension {
+    typedef typename T::Feature_dimension type;
   };
 
   template <typename K>
diff --git a/Kernel_d/include/CGAL/Kernel_d/Aff_transformation_d.h b/Kernel_d/include/CGAL/Kernel_d/Aff_transformation_d.h
index 68fd07eb02d..41e550107df 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Aff_transformation_d.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Aff_transformation_d.h
@@ -18,17 +18,21 @@
 // $URL$
 // $Id$
 // 
-//
 // Author(s)     : Michael Seel <seel@mpi-sb.mpg.de>
 
 #ifndef CGAL_AFF_TRANSFORMATION_D_H
 #define CGAL_AFF_TRANSFORMATION_D_H
 
+#include <CGAL/Dimension.h>
+
 CGAL_BEGIN_NAMESPACE
 
 template <class pR>
 class Aff_transformation_d : public pR::Aff_transformation_d_base
 { public:
+
+  typedef CGAL::Dynamic_dimension_tag            Ambiant_dimension;
+
   typedef typename pR::Aff_transformation_d_base Base;
   typedef Aff_transformation_d<pR>               Self;
   typedef pR R;
diff --git a/Kernel_d/include/CGAL/Kernel_d/Direction_d.h b/Kernel_d/include/CGAL/Kernel_d/Direction_d.h
index 407e78ca216..b197f208fdb 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Direction_d.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Direction_d.h
@@ -20,14 +20,21 @@
 // 
 //
 // Author(s)     : Michael Seel
+
 #ifndef CGAL_DIRECTION_D_H
 #define CGAL_DIRECTION_D_H
 
+#include <CGAL/Dimension.h>
+
 CGAL_BEGIN_NAMESPACE
 
 template <class pR>
 class Direction_d : public pR::Direction_d_base
 { public:
+
+  typedef CGAL::Dynamic_dimension_tag Ambiant_dimension;
+  typedef CGAL::Dimension_tag<0>      Feature_dimension;
+
   typedef typename pR::Direction_d_base Base;
   typedef Direction_d<pR>               Self;
   typedef pR R;
diff --git a/Kernel_d/include/CGAL/Kernel_d/Hyperplane_d.h b/Kernel_d/include/CGAL/Kernel_d/Hyperplane_d.h
index 0143696951c..9589a9cf025 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Hyperplane_d.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Hyperplane_d.h
@@ -24,12 +24,18 @@
 #ifndef CGAL_HYPERPLANE_D_H
 #define CGAL_HYPERPLANE_D_H
 
+#include <CGAL/Dimension.h>
+
 CGAL_BEGIN_NAMESPACE
 
 template <class pR>
 class Hyperplane_d : public pR::Hyperplane_d_base
 {
 public:
+
+  typedef CGAL::Dynamic_dimension_tag Ambiant_dimension;
+  typedef CGAL::Dynamic_dimension_tag Feature_dimension;
+
   typedef typename pR::Hyperplane_d_base Base;
   typedef Hyperplane_d<pR>               Self;
   typedef pR R;
diff --git a/Kernel_d/include/CGAL/Kernel_d/Iso_box_d.h b/Kernel_d/include/CGAL/Kernel_d/Iso_box_d.h
index 074f152a7fa..577a35e2cd2 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Iso_box_d.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Iso_box_d.h
@@ -27,6 +27,7 @@
 #include <CGAL/basic.h>
 #include <CGAL/Handle_for.h>
 #include <CGAL/representation_tags.h> 
+#include <CGAL/Dimension.h>
 #include <functional>
 #include <algorithm>
 #include <numeric>
@@ -311,6 +312,9 @@ namespace CGAL {
     
 public:
 
+    typedef CGAL::Dynamic_dimension_tag Ambiant_dimension;
+    typedef CGAL::Dynamic_dimension_tag Feature_dimension;
+
     Iso_box_d() {}
     
     Iso_box_d(const Point_d& p, const Point_d& q)
diff --git a/Kernel_d/include/CGAL/Kernel_d/Line_d.h b/Kernel_d/include/CGAL/Kernel_d/Line_d.h
index 5313cba709a..afcf2a7e22b 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Line_d.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Line_d.h
@@ -27,6 +27,7 @@
 #include <CGAL/Kernel_d/Pair_d.h> 
 #include <CGAL/Kernel_d/Segment_d.h> 
 #include <CGAL/Kernel_d/Ray_d.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -50,6 +51,10 @@ An instance of data type |Line_d| is an oriented line in
 $d$-dimensional Euclidian space.}*/
 
 public: 
+
+  typedef CGAL::Dynamic_dimension_tag Ambiant_dimension;
+  typedef CGAL::Dimension_tag<1>      Feature_dimension;
+
 /*{\Mtypes 5}*/
 typedef p_R R;
 /*{\Mtypemember the representation type.}*/
diff --git a/Kernel_d/include/CGAL/Kernel_d/Point_d.h b/Kernel_d/include/CGAL/Kernel_d/Point_d.h
index 2b07aa38434..040c5dd1c5b 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Point_d.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Point_d.h
@@ -20,9 +20,12 @@
 // 
 //
 // Author(s)     : Michael Seel
+
 #ifndef CGAL_POINT_D_H
 #define CGAL_POINT_D_H
 
+#include <CGAL/Dimension.h>
+
 CGAL_BEGIN_NAMESPACE
 
 template <class pR>
@@ -37,6 +40,9 @@ private:
   typedef typename R::LA LA;
 public:
 
+  typedef CGAL::Dynamic_dimension_tag Ambiant_dimension;
+  typedef CGAL::Dimension_tag<0>      Feature_dimension;
+
   Point_d(int d=0) : Base(d) {}
   Point_d(int d, const Origin &o) : Base(d,o) {}
 
diff --git a/Kernel_d/include/CGAL/Kernel_d/Ray_d.h b/Kernel_d/include/CGAL/Kernel_d/Ray_d.h
index ad6ac38d0c0..de2e548a8ab 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Ray_d.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Ray_d.h
@@ -20,12 +20,14 @@
 // 
 //
 // Author(s)     : Michael Seel
+
 #ifndef CGAL_RAY_D_H
 #define CGAL_RAY_D_H
 
 #include <CGAL/Kernel_d/Pair_d.h>
 #include <CGAL/Kernel_d/Segment_d.h> 
 #include <CGAL/Kernel_d/Line_d.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -51,6 +53,10 @@ Euclidian space. It starts in a point called the source of |\Mvar| and
 it goes to infinity.}*/
 
 public: 
+
+  typedef CGAL::Dynamic_dimension_tag Ambiant_dimension;
+  typedef CGAL::Dimension_tag<1>      Feature_dimension;
+
 /*{\Mtypes 4}*/
 typedef p_R R;
 /*{\Mtypemember the representation type.}*/
diff --git a/Kernel_d/include/CGAL/Kernel_d/Segment_d.h b/Kernel_d/include/CGAL/Kernel_d/Segment_d.h
index 604432d35e3..a2e7aa6bb3d 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Segment_d.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Segment_d.h
@@ -20,12 +20,14 @@
 // 
 //
 // Author(s)     : Michael Seel
+
 #ifndef CGAL_SEGMENT_D_H
 #define CGAL_SEGMENT_D_H 
 
 #include <CGAL/Kernel_d/Pair_d.h> 
 #include <CGAL/Kernel_d/Line_d.h> 
 #include <CGAL/Kernel_d/Ray_d.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -53,6 +55,10 @@ $p$ and $q$. $p$ is called the source point and $q$ is called
 the target point of $s$, both points are called endpoints of $s$. A
 segment whose endpoints are equal is called \emph{degenerate}.}*/
 public: 
+
+  typedef CGAL::Dynamic_dimension_tag Ambiant_dimension;
+  typedef CGAL::Dimension_tag<1>      Feature_dimension;
+
 /*{\Mtypes 5}*/
 typedef p_R R;
 /*{\Mtypemember the representation type.}*/
diff --git a/Kernel_d/include/CGAL/Kernel_d/Sphere_d.h b/Kernel_d/include/CGAL/Kernel_d/Sphere_d.h
index 9c6d7951536..06d895b2eea 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Sphere_d.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Sphere_d.h
@@ -20,11 +20,13 @@
 // 
 //
 // Author(s)     : Michael Seel
+
 #ifndef CGAL_SPHERE_D_H
 #define CGAL_SPHERE_D_H
 
 #include <CGAL/basic.h>
 #include <vector>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -77,6 +79,9 @@ set of defining points to be legal.  The orientation of $S$ is equal
 to the orientation of the defining points, i.e., |orientation(A)|. }*/
 
 public: 
+  typedef CGAL::Dynamic_dimension_tag Ambiant_dimension;
+  typedef CGAL::Dynamic_dimension_tag Feature_dimension;
+
 /*{\Mtypes 4}*/
 
 typedef Sphere_d_rep<R_>  Rep;
diff --git a/Kernel_d/include/CGAL/Kernel_d/Vector_d.h b/Kernel_d/include/CGAL/Kernel_d/Vector_d.h
index 75d05412024..0bc4409f72d 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Vector_d.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Vector_d.h
@@ -17,17 +17,23 @@
 //
 // $URL$
 // $Id$
-// 
 //
 // Author(s)     : Michael Seel
+
 #ifndef CGAL_VECTOR_D_H
 #define CGAL_VECTOR_D_H
 
+#include <CGAL/Dimension.h>
+
 CGAL_BEGIN_NAMESPACE
  
 template <class pR>
 class Vector_d : public pR::Vector_d_base
 { public:
+
+  typedef CGAL::Dynamic_dimension_tag Ambiant_dimension;
+  typedef CGAL::Dimension_tag<0>      Feature_dimension;
+
   typedef typename pR::Vector_d_base Base;
   typedef Vector_d<pR>               Self;
   typedef pR R;
diff --git a/Principal_component_analysis/include/CGAL/PCA_util.h b/Principal_component_analysis/include/CGAL/PCA_util.h
index 6d32b4a6006..e3de021e356 100644
--- a/Principal_component_analysis/include/CGAL/PCA_util.h
+++ b/Principal_component_analysis/include/CGAL/PCA_util.h
@@ -22,7 +22,7 @@
 #include <CGAL/basic.h>
 #include <CGAL/Object.h>
 #include <CGAL/Linear_algebraCd.h>
-#include <CGAL/Dimension_tag.h>
+#include <CGAL/Dimension.h>
 
 CGAL_BEGIN_NAMESPACE
 
diff --git a/Principal_component_analysis/include/CGAL/centroid.h b/Principal_component_analysis/include/CGAL/centroid.h
index e2b7a5dccdf..18133b76225 100644
--- a/Principal_component_analysis/include/CGAL/centroid.h
+++ b/Principal_component_analysis/include/CGAL/centroid.h
@@ -25,7 +25,7 @@
 #include <iterator>
 #include <CGAL/Kernel_traits.h>
 #include <CGAL/Kernel/Dimension_utils.h>
-#include <CGAL/Dimension_tag.h>
+#include <CGAL/Dimension.h>
 
 #include <list>
 // Functions to compute the centroid of N points.
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h
index 20c27325f8e..86082c66122 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h
@@ -28,7 +28,7 @@
 #include <CGAL/linear_least_squares_fitting_triangles_2.h>
 #include <CGAL/linear_least_squares_fitting_circles_2.h>
 #include <CGAL/linear_least_squares_fitting_rectangles_2.h>
-#include <CGAL/Dimension_tag.h>
+#include <CGAL/Dimension.h>
 
 #include <iterator>
 
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h
index 72d64c7c127..fd696ad3ebd 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h
@@ -31,7 +31,7 @@
 #include <CGAL/linear_least_squares_fitting_tetrahedra_3.h>
 #include <CGAL/linear_least_squares_fitting_spheres_3.h>
 
-#include <CGAL/Dimension_tag.h>
+#include <CGAL/Dimension.h>
 
 #include <iterator>
 #include <list>