diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_3.h
index 7a04f837092..dce2d467b1e 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_3.h
@@ -161,6 +161,9 @@ public:
   bool is_even() const { return this->Ptr()->is_even(); }
   bool is_odd() const { return  ! (this->Ptr()->is_even()); }
 
+  bool is_translation() const { return this->Ptr()->is_translation(); }
+
+
   FT cartesian(int i, int j) const { return this->Ptr()->cartesian(i,j); }
   FT homogeneous(int i, int j) const { return cartesian(i,j); }
   FT m(int i, int j) const { return cartesian(i,j); }
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_rep_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_rep_3.h
index 406cb7accca..2af5a97cedd 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_rep_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_rep_3.h
@@ -54,6 +54,7 @@ public:
   virtual Aff_transformation_3 inverse() const = 0;
   virtual Aff_transformation_3 transpose() const = 0;
   virtual bool                 is_even() const = 0;
+  virtual bool                 is_translation() const = 0;
   virtual FT                   cartesian(int i, int j) const = 0;
   virtual std::ostream         &print(std::ostream &os) const = 0;
 };
@@ -144,6 +145,12 @@ public:
                                   t31, t32, t33) == POSITIVE;
   }
 
+
+  virtual bool is_translation() const
+  {
+    return false;
+  }
+
   virtual FT cartesian(int i, int j) const
   {
     switch (i)
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Scaling_rep_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Scaling_rep_3.h
index 061f1806a9e..d90928efddb 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Scaling_rep_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Scaling_rep_3.h
@@ -121,6 +121,12 @@ public:
     return true;
   }
 
+  virtual bool is_translation() const
+  {
+    return false;
+  }
+
+
   virtual FT cartesian(int i, int j) const
   {
     if (i!=j) return FT(0);
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Translation_rep_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Translation_rep_3.h
index 6377c1a3d8a..9f0d718a64e 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Translation_rep_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Translation_rep_3.h
@@ -125,6 +125,11 @@ public:
     return true;
   }
 
+  virtual bool is_translation() const
+  {
+    return true;
+  }
+
   virtual FT cartesian(int i, int j) const
   {
     if (j==i) return FT(1);
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h b/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h
index b67c4f024a3..1ee88421490 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h
@@ -87,6 +87,9 @@ public:
 
   virtual  FT
            cartesian(int i, int j) const = 0;
+
+  virtual  bool
+           is_translation() const = 0;
 };
 
 template < class R_ >
@@ -212,6 +215,12 @@ public:
            is_even() const
            { return true; }
 
+  virtual  bool
+           is_translation() const
+           {
+             return false;
+           }
+
   virtual  RT
            homogeneous(int i, int j) const
            { return (i==j) ? RT(1) : RT(0); }
@@ -693,6 +702,12 @@ bool
 Translation_repH3<R>::is_even() const
 { return true; }
 
+template < class R >
+inline
+bool
+Translation_repH3<R>::is_translation() const
+{ return true; }
+
 template < class R >
 CGAL_KERNEL_LARGE_INLINE
 typename Translation_repH3<R>::RT
diff --git a/Nef_3/include/CGAL/Nef_polyhedron_3.h b/Nef_3/include/CGAL/Nef_polyhedron_3.h
index 8a2e1e16520..c1a0791152f 100644
--- a/Nef_3/include/CGAL/Nef_polyhedron_3.h
+++ b/Nef_3/include/CGAL/Nef_polyhedron_3.h
@@ -1710,6 +1710,8 @@ protected:
     bool ninety = is_90degree_rotation(aff);
     bool scale = is_scaling(aff);
 
+    bool translate = aff.is_translation();
+
     Vertex_iterator vi;
     CGAL_forall_vertices( vi, snc()) {
 
@@ -1726,8 +1728,10 @@ protected:
         vertex_list.push_back(vi);
       } else {
         vi->point() = vi->point().transform( aff);
-        SM_decorator sdeco(&*vi);
-        sdeco.transform( linear);
+        if(! translate){
+          SM_decorator sdeco(&*vi);
+          sdeco.transform( linear);
+        }
       }
     }