diff --git a/Cubical_gaussian_map_3/include/CGAL/Cubical_gaussian_map_3.h b/Cubical_gaussian_map_3/include/CGAL/Cubical_gaussian_map_3.h
index 28a58340156..1b6d9bb0dc3 100644
--- a/Cubical_gaussian_map_3/include/CGAL/Cubical_gaussian_map_3.h
+++ b/Cubical_gaussian_map_3/include/CGAL/Cubical_gaussian_map_3.h
@@ -449,7 +449,7 @@ protected:
       }
     } else if (proj_normal1.num_faces() == 3) {
       unsigned index = Cgm::get_corner_index(faces_mask1, id);
-      CGAL_assertion(index < NUM_CORNERS);
+      CGAL_assertion(index < Cgm::NUM_CORNERS);
       Arr_vertex_handle v =
         m_cgm.m_corner_vertices[id][index];
       /*! \todo Set the entire cyclic chain of 3 vertices, and not just the
@@ -492,7 +492,7 @@ protected:
       }
     } else if (proj_normal2.num_faces() == 3) {
       unsigned index = Cgm::get_corner_index(faces_mask2, id);
-      CGAL_assertion(index < NUM_CORNERS);
+      CGAL_assertion(index < Cgm::NUM_CORNERS);
       Arr_vertex_handle v =
         m_cgm.m_corner_vertices[id][index];
       /*! \todo Set the entire cyclic chain of 3 vertices, and not just the
diff --git a/Cubical_gaussian_map_3/include/CGAL/IO/Cgm_iostream.h b/Cubical_gaussian_map_3/include/CGAL/IO/Cgm_iostream.h
index b4cb9dbe8e5..ce7b7874988 100644
--- a/Cubical_gaussian_map_3/include/CGAL/IO/Cgm_iostream.h
+++ b/Cubical_gaussian_map_3/include/CGAL/IO/Cgm_iostream.h
@@ -25,6 +25,10 @@
  */
 
 #include <CGAL/basic.h>
+#include <CGAL/Cubical_gaussian_map_3.h>
+#include <CGAL/IO/Arr_iostream.h>
+
+#include <iostream>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -51,18 +55,18 @@ operator<<(std::ostream & os,
  * \param os the output stream
  * \param cgm the Cubical_gaussian_map_3 object
  */
-template <class T_Traits,
+template <class Kernel,
 #ifndef CGAL_CFG_NO_TMPL_IN_TMPL_PARAM
           template <class T>
 #endif
           class T_Dcel>
 inline
 std::ostream & operator<<(std::ostream & os,
-                          const Cubical_gaussian_map_3<T_Traits,T_Dcel> & cgm) 
+                          const Cubical_gaussian_map_3<Kernel,T_Dcel> & cgm) 
 {
-  typedef Cubical_gaussian_map_3<T_Traits,T_Dcel> Cgm;
-  for (unsigned int i = 0; i < Cubical_gaussian_map_3::NUM_FACES; ++i) {
-    const typename Cgm::Arrangement & arr = cgm.get_arrangement(i);
+  typedef Cubical_gaussian_map_3<Kernel,T_Dcel> Cgm;
+  for (unsigned int i = 0; i < Cgm::NUM_FACES; ++i) {
+    const typename Cgm::Arrangement & arr = cgm.arrangement(i);
     os << arr;
   }
   return os;
@@ -72,15 +76,15 @@ std::ostream & operator<<(std::ostream & os,
  * \param is the input stream
  * \param cgm the Cubical_gaussian_map_3 object
  */
-template <class T_Traits,
+template <class Kernel,
 #ifndef CGAL_CFG_NO_TMPL_IN_TMPL_PARAM
           template <class T>
 #endif
           class T_Dcel>
 inline std::istream & operator>>(std::istream & is,
-                                 Cubical_gaussian_map_3<T_Traits,T_Dcel> & cgm)
+                                 Cubical_gaussian_map_3<Kernel,T_Dcel> & cgm)
 {
-  typedef Cubical_gaussian_map_3<T_Traits,T_Dcel> Cgm;
+  typedef Cubical_gaussian_map_3<Kernel,T_Dcel> Cgm;
   for (unsigned int i = 0; i < Cubical_gaussian_map_3::NUM_FACES; ++i) {
     const typename Cgm::Arrangement & arr = cgm.get_arrangement(i);
     arr >> is;
diff --git a/Cubical_gaussian_map_3/include/CGAL/IO/Polyhedral_cgm_iostream.h b/Cubical_gaussian_map_3/include/CGAL/IO/Polyhedral_cgm_iostream.h
index 2652591d784..b8515decc2a 100644
--- a/Cubical_gaussian_map_3/include/CGAL/IO/Polyhedral_cgm_iostream.h
+++ b/Cubical_gaussian_map_3/include/CGAL/IO/Polyhedral_cgm_iostream.h
@@ -17,14 +17,18 @@
 //
 // Author(s)     : Efi Fogel          <efif@post.tau.ac.il>
 
-#ifndef CGAL_CGM_IOSTREAM_H
-#define CGAL_CGM_IOSTREAM_H
+#ifndef CGAL_POLYHEDRAL_CGM_IOSTREAM_H
+#define CGAL_POLYHEDRAL_CGM_IOSTREAM_H
 
 /*! \file Implmentation of importer and exporter IO operations of a
  * Polyhedral_cgm object
  */
 
 #include <CGAL/basic.h>
+#include <CGAL/Polyhedral_cgm.h>
+#include <CGAL/IO/Cgm_iostream.h>
+
+#include <iostream>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -37,11 +41,11 @@ template <class Kernel,
           template <class T>
 #endif
           class T_Dcel>
-inline
-std::ostream & operator<<(std::ostream & os,
-                          const Polyhedral_cgm<Kernel,T_Dcel> & cgm) 
+inline std::ostream & operator<<(std::ostream & os,
+                                 const Polyhedral_cgm<Kernel,T_Dcel> & cgm) 
 {
-  os << static_cast<Cubical_gaussian_map_3<Kernel,T_Dcel>(cgm);
+  const Cubical_gaussian_map_3<Kernel,T_Dcel> * tmp = &cgm;
+  os << *tmp;
   return os;
 }
 
diff --git a/Cubical_gaussian_map_3/include/CGAL/Polyhedral_cgm.h b/Cubical_gaussian_map_3/include/CGAL/Polyhedral_cgm.h
index d622869037e..f6aa63374ea 100644
--- a/Cubical_gaussian_map_3/include/CGAL/Polyhedral_cgm.h
+++ b/Cubical_gaussian_map_3/include/CGAL/Polyhedral_cgm.h
@@ -64,8 +64,7 @@ CGAL_BEGIN_NAMESPACE
 /*!
  */
 template <class PolyhedralCgm,
-          class Polyhedron =
-            Polyhedral_cgm_default_polyhedron_3<PolyhedralCgm>,
+          class Polyhedron = Polyhedral_cgm_polyhedron_3<PolyhedralCgm>,
           class Visitor = Polyhedral_cgm_initializer_visitor<PolyhedralCgm> >
 class Polyhedral_cgm_initializer :
   public Cgm_initializer<typename PolyhedralCgm::Base>
@@ -712,13 +711,26 @@ public:
     } while(hec != hec_begin);
   }
   
-  /*! Compute the minkowski sum
+  /*! Compute the minkowski sum of a range of objects of type Polyhedral_cgm
    */
   template <class CgmIterator>  
-  void minkowsi_sum(CgmIterator begin, CgmIterator end)
+  void minkowski_sum(CgmIterator begin, CgmIterator end)
+  {
+    Polyhedral_cgm * cgm1 = *begin++;
+    Polyhedral_cgm * cgm2 = *begin;
+    minkowski_sum(cgm1, cgm2);
+  }
+
+  /*! Compute the minkowski sum of 2 objects of type Polyhedral_cgm
+   * \param cgm1 the first Polyhedral_cgm object
+   * \param cgm2 the second Polyhedral_cgm object
+   */
+  template <>  
+  void minkowski_sum<Polyhedral_cgm *>(Polyhedral_cgm * cgm1,
+                                       Polyhedral_cgm * cgm2)
   {
     // Compute the overlays:
-    overlay(begin, end);
+    overlay(cgm1, cgm2);
 
     // Initialize the corners:
     init_corners();
@@ -748,18 +760,17 @@ public:
     // print_stat();
   }
 
-  /*! Compute the overlay
+  /*! Compute the overlay of the respective 6 face pairs of 2 Polyhedral_cgm
+   * objects.
+   * \param cgm1 the first Polyhedral_cgm object
+   * \param cgm2 the second Polyhedral_cgm object
    */
-  template <class CgmIterator>  
-  void overlay(CgmIterator & begin, CgmIterator & end)
+  void overlay(Polyhedral_cgm * cgm1, Polyhedral_cgm * cgm2)
   {
-    Polyhedral_cgm * gm1 = *begin++;
-    Polyhedral_cgm * gm2 = *begin;
-
     for (unsigned int i = 0; i < NUM_FACES; ++i) {
       Arr & arr = m_arrangements[i];
-      Arr & arr1 = gm1->m_arrangements[i];
-      Arr & arr2 = gm2->m_arrangements[i];
+      Arr & arr1 = cgm1->m_arrangements[i];
+      Arr & arr2 = cgm2->m_arrangements[i];
 
 #if 0
       Arr_halfedge_const_iterator hi;
diff --git a/Cubical_gaussian_map_3/include/CGAL/Polyhedral_cgm_initializer_visitor.h b/Cubical_gaussian_map_3/include/CGAL/Polyhedral_cgm_initializer_visitor.h
index 88a5133d293..f72bc62f951 100644
--- a/Cubical_gaussian_map_3/include/CGAL/Polyhedral_cgm_initializer_visitor.h
+++ b/Cubical_gaussian_map_3/include/CGAL/Polyhedral_cgm_initializer_visitor.h
@@ -24,8 +24,8 @@
 
 CGAL_BEGIN_NAMESPACE
 
-template<class Cgm,
-         class Polyhedron = Polyhedral_cgm_default_polyhedron_3<Cgm> >
+template<class PolyhedralCgm,
+         class Polyhedron = Polyhedral_cgm_polyhedron_3<PolyhedralCgm> >
 class Polyhedral_cgm_initializer_visitor {
 public:
   typedef typename Polyhedron::Vertex_const_handle
@@ -35,10 +35,10 @@ public:
   typedef typename Polyhedron::Facet_const_handle
     Polyhedron_facet_const_handle;
 
-  typedef typename Cgm::Arr_vertex_handle               Arr_vertex_handle;
-  typedef typename Cgm::Arr_halfedge_handle             Arr_halfedge_handle;
-  typedef typename Cgm::Arr_face_handle                 Arr_face_handle;
-  typedef typename Cgm::Arr_face_const_handle           Arr_face_const_handle;
+  typedef typename PolyhedralCgm::Arr_vertex_handle     Arr_vertex_handle;
+  typedef typename PolyhedralCgm::Arr_halfedge_handle   Arr_halfedge_handle;
+  typedef typename PolyhedralCgm::Arr_face_handle       Arr_face_handle;
+  typedef typename PolyhedralCgm::Arr_face_const_handle Arr_face_const_handle;
 
   /*! Pass information from a polyhedron vertex to its dual - a cgm-face */
   virtual void update_dual_vertex(Polyhedron_vertex_const_handle src,
diff --git a/Cubical_gaussian_map_3/include/CGAL/Polyhedral_cgm_polyhedron_3.h b/Cubical_gaussian_map_3/include/CGAL/Polyhedral_cgm_polyhedron_3.h
index 698ada55c34..4b07f16d88b 100644
--- a/Cubical_gaussian_map_3/include/CGAL/Polyhedral_cgm_polyhedron_3.h
+++ b/Cubical_gaussian_map_3/include/CGAL/Polyhedral_cgm_polyhedron_3.h
@@ -199,12 +199,12 @@ struct Polyhedral_cgm_polyhedron_items : public CGAL::Polyhedron_items_3 {
  * based on the new items type.
  */
 template <class Cgm>
-struct Polyhedral_cgm_default_polyhedron_3 :
+struct Polyhedral_cgm_polyhedron_3 :
   public CGAL::Polyhedron_3<CGAL::Polyhedron_traits_with_normals_3<typename Cgm::Kernel>,
                             Polyhedral_cgm_polyhedron_items<Cgm> >
 {
   /*! Constructor */
-  Polyhedral_cgm_default_polyhedron_3() {}
+  Polyhedral_cgm_polyhedron_3() {}
 };
 
 CGAL_END_NAMESPACE