diff --git a/Triangulation/TODO b/Triangulation/TODO
index 97f0b5205b5..4ac35cea916 100644
--- a/Triangulation/TODO
+++ b/Triangulation/TODO
@@ -19,16 +19,16 @@ Pure_complex_locate_type            Triangulation_locate_type
 Pure_complex_simplex                Triangulation_full_cell
 Pure_complex_vertex                 Triangulation_vertex
 RegularComplexTraits                RegularTriangulationTraits 
-Regular_complex                     RegularTriangulation
+Regular_complex                     Regular_triangulation
 
 code
 
-/Pure_complex/Triangulation/
-/Delaunay_complex/Delaunay_triangulation/
-/Simplex/Full_cell/
-/simplex/full_cell/
-/number_of_simplices/number_of_full_cells/
-/gather_simplices/gather_full_cells/
+[DONE] /Pure_complex/Triangulation/
+[DONE] /Delaunay_complex/Delaunay_triangulation/
+[DONE] /Simplex/Full_cell/
+[DONE] /simplex/full_cell/
+[DONE] /number_of_simplices/number_of_full_cells/
+[DONE] /gather_simplices/gather_full_cells/
 /gather_incident_simplices/incident_full_cells/
 /gather_adjacent_simplices/compute_star/
 /gather_incident_simplices/incident_simplices/
@@ -42,7 +42,7 @@ code
 
 is_boundary_facet
 
-to remove (comment)
+to remove (comment) (sam: I find them useful!)
 gather_incident_faces
 gather_incident_upper_faces
 
diff --git a/Triangulation/include/CGAL/Convex_hull.h b/Triangulation/include/CGAL/Convex_hull.h
index 363d73ee283..d048dc0e2e2 100644
--- a/Triangulation/include/CGAL/Convex_hull.h
+++ b/Triangulation/include/CGAL/Convex_hull.h
@@ -18,7 +18,7 @@
 /* RANDOM DESIGN IDEAS:
 - Use a policy tag to choose for incremental with inserts only or
   incremental with  removals and inserts.
-  In the first case: use Pure_complex for storage.
+  In the first case: use Triangulation for storage.
   In the second case: use Delaunay !
     In this second case, we must keeps the points that are inserted in the hull,
     as they may become part of the boundary later on, when some points are removed.
@@ -33,18 +33,18 @@ namespace CGAL {
 template <  class CHTraits, class TDS_ = Default >
 class Convex_hull
 {
-    typedef typename Ambient_dimension<typename PCTraits::Point_d>::type
+    typedef typename Ambient_dimension<typename CHTraits::Point_d>::type
                                                     Ambient_dimension_;
-    typedef typename Default::Get<TDS_, Pure_complex_data_structure
+    typedef typename Default::Get<TDS_, Triangulation_data_structure
                     <   Ambient_dimension_,
-                        Pure_complex_vertex<PCTraits>,
-                        Pure_complex_simplex<PCTraits> >
+                        Triangulation_vertex<CHTraits>,
+                        Triangulation_full_cell<CHTraits> >
                         >::type                     TDS;
-    typedef Pure_complex<PCTraits, TDS_>           Self;
+    typedef Convex_hull<CHTraits, TDS_>           Self;
 
-    typedef typename PCTraits::Coaffine_orientation_d
+    typedef typename CHTraits::Coaffine_orientation_d
                                                     Coaffine_orientation_d;
-    typedef typename PCTraits::Orientation_d        Orientation_d;
+    typedef typename CHTraits::Orientation_d        Orientation_d;
 
 public:
 };
diff --git a/Triangulation/include/CGAL/internal/Triangulation/utilities.h b/Triangulation/include/CGAL/internal/Triangulation/utilities.h
index 9e73599a3f7..5cea13101f4 100644
--- a/Triangulation/include/CGAL/internal/Triangulation/utilities.h
+++ b/Triangulation/include/CGAL/internal/Triangulation/utilities.h
@@ -66,17 +66,17 @@ public:
     }
 };
 
-template< class PC >
+template< class T >
 struct Compare_vertices_for_upper_face
 {
-    typedef typename PC::Vertex_const_handle VCH;
+    typedef typename T::Vertex_const_handle VCH;
 
-    const PC & pc_;
+    const T & t_;
 
 public:
 
-    Compare_vertices_for_upper_face(const PC & pc)
-    : pc_(pc)
+    Compare_vertices_for_upper_face(const T & t)
+    : t_(t)
     {}
 
     explicit Compare_vertices_for_upper_face();
@@ -85,40 +85,40 @@ public:
     {
         if( left == right )
             return false;
-        if( pc_.is_infinite(left) )
+        if( t_.is_infinite(left) )
             return true;
-        if( pc_.is_infinite(right) )
+        if( t_.is_infinite(right) )
             return false;
         return left < right;
     }
 };
 
-template< class PC >
+template< class T >
 struct Compare_points_for_perturbation
 {
-    typedef typename PC::Point_d Point;
+    typedef typename T::Point_d Point;
 
-    const PC & pc_;
+    const T & t_;
 
 public:
 
-    Compare_points_for_perturbation(const PC & pc)
-    : pc_(pc)
+    Compare_points_for_perturbation(const T & t)
+    : t_(t)
     {}
 
     explicit Compare_points_for_perturbation();
 
     bool operator()(const Point * left, const Point * right) const
     {
-        return (SMALLER == pc_.geom_traits().compare_lexicographically_d_object()(*left, *right));
+        return (SMALLER == t_.geom_traits().compare_lexicographically_d_object()(*left, *right));
     }
 };
 
-template< class PC >
+template< class T >
 struct Point_from_pointer
 {
-    typedef const typename PC::Point_d *   argument_type;
-    typedef const typename PC::Point_d     result_type;
+    typedef const typename T::Point_d *   argument_type;
+    typedef const typename T::Point_d     result_type;
     result_type & operator()(argument_type & x) const 
     {
         return (*x);