diff --git a/Linear_cell_complex/examples/Linear_cell_complex/exemple_incremental_builder.cpp b/Linear_cell_complex/examples/Linear_cell_complex/exemple_incremental_builder.cpp
index b80c4cc4a3d..155a37e8475 100644
--- a/Linear_cell_complex/examples/Linear_cell_complex/exemple_incremental_builder.cpp
+++ b/Linear_cell_complex/examples/Linear_cell_complex/exemple_incremental_builder.cpp
@@ -94,9 +94,9 @@ public:
     }
 };
 
-typedef CGAL::Combinatorial_map_with_points<2,3> LCC_3;
-typedef LCC_3::Dart_handle                     Dart_handle;
-typedef LCC_3::Point                           Point;
+typedef CGAL::Linear_cell_complex<2,3> LCC_3;
+typedef LCC_3::Dart_handle             Dart_handle;
+typedef LCC_3::Point                   Point;
 
 typedef CGAL::Polyhedron_3<LCC_3::Traits>  Polyhedron;
 typedef Polyhedron::HalfedgeDS             HalfedgeDS;
diff --git a/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_3.cpp b/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_3.cpp
index b45e11e99f2..800a1f2db25 100644
--- a/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_3.cpp
+++ b/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_3.cpp
@@ -4,10 +4,10 @@
 #include <iostream>
 #include <algorithm>
 
-typedef CGAL::Combinatorial_map_with_points<3> LCC_3;
-typedef LCC_3::Dart_handle                     Dart_handle;
-typedef LCC_3::Point                           Point;
-typedef LCC_3::FT                              FT;
+typedef CGAL::Linear_cell_complex<3> LCC_3;
+typedef LCC_3::Dart_handle           Dart_handle;
+typedef LCC_3::Point                 Point;
+typedef LCC_3::FT                    FT;
 
 // Functor used to display all the vertices of a given volume
 template<class LCC> 
diff --git a/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_3_with_colored_vertices.cpp b/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_3_with_colored_vertices.cpp
index 690ecc338d6..60ee765803e 100644
--- a/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_3_with_colored_vertices.cpp
+++ b/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_3_with_colored_vertices.cpp
@@ -47,28 +47,28 @@ struct Myitem
 
 typedef CGAL::Linear_cell_complex_traits
          <3, CGAL::Exact_predicates_inexact_constructions_kernel> Traits;
-typedef CGAL::Combinatorial_map_with_points<3,3,Traits,Myitem> LCC_3;
-typedef LCC_3::Dart_handle                             Dart_handle;
-typedef LCC_3::Point                                   Point;
-typedef LCC_3::FT                                      FT;
+typedef CGAL::Linear_cell_complex<3,3,Traits,Myitem> LCC_3;
+typedef LCC_3::Dart_handle                           Dart_handle;
+typedef LCC_3::Point                                 Point;
+typedef LCC_3::FT                                    FT;
 
 Dart_handle make_iso_cuboid(LCC_3& lcc, const Point& basepoint, FT lg)
 {
-	return lcc.make_hexahedron(basepoint,
-                             LCC_3::Construct_translated_point()(basepoint,
-                                                                 LCC_3::Vector(lg,0,0)),
-                             LCC_3::Construct_translated_point()(basepoint,
-                                                                 LCC_3::Vector(lg,lg,0)),
-                             LCC_3::Construct_translated_point()(basepoint,
-                                                                 LCC_3::Vector(0,lg,0)),
-                             LCC_3::Construct_translated_point()(basepoint,
-                                                                 LCC_3::Vector(0,lg,lg)),
-                             LCC_3::Construct_translated_point()(basepoint,
-                                                                 LCC_3::Vector(0,0,lg)),
-                             LCC_3::Construct_translated_point()(basepoint,
-                                                                 LCC_3::Vector(lg,0,lg)),
-                             LCC_3::Construct_translated_point()(basepoint,
-                                                                 LCC_3::Vector(lg,lg,lg)));
+  return lcc.make_hexahedron(basepoint,
+                             LCC_3::Traits::Construct_translated_point()(basepoint,
+                                                                 LCC_3::Traits::Vector(lg,0,0)),
+                             LCC_3::Traits::Construct_translated_point()(basepoint,
+                                                                 LCC_3::Traits::Vector(lg,lg,0)),
+                             LCC_3::Traits::Construct_translated_point()(basepoint,
+                                                                 LCC_3::Traits::Vector(0,lg,0)),
+                             LCC_3::Traits::Construct_translated_point()(basepoint,
+                                                                 LCC_3::Traits::Vector(0,lg,lg)),
+                             LCC_3::Traits::Construct_translated_point()(basepoint,
+                                                                 LCC_3::Traits::Vector(0,0,lg)),
+                             LCC_3::Traits::Construct_translated_point()(basepoint,
+                                                                 LCC_3::Traits::Vector(lg,0,lg)),
+                             LCC_3::Traits::Construct_translated_point()(basepoint,
+                                                                 LCC_3::Traits::Vector(lg,lg,lg)));
 }
 
 int main()
diff --git a/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_4.cpp b/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_4.cpp
index b81dd368d02..b32aafe3f14 100644
--- a/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_4.cpp
+++ b/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_4.cpp
@@ -4,11 +4,11 @@
 #include <iostream>
 #include <vector>
 
-typedef CGAL::Combinatorial_map_with_points<4,5> LCC_4;
-typedef LCC_4::Dart_handle Dart_handle;
-typedef LCC_4::Point Point;
-typedef LCC_4::Vector Vector;
-typedef LCC_4::FT FT;
+typedef CGAL::Linear_cell_complex<4,5> LCC_4;
+typedef LCC_4::Dart_handle             Dart_handle;
+typedef LCC_4::Point                   Point;
+typedef LCC_4::Vector                  Vector;
+typedef LCC_4::FT                      FT;
 
 // Functor used to display all the vertices of a given volume
 template<class LCC> 
diff --git a/Linear_cell_complex/examples/Linear_cell_complex/map_3_iterators.cpp b/Linear_cell_complex/examples/Linear_cell_complex/map_3_iterators.cpp
index afd07f0aed2..860a5e6831e 100644
--- a/Linear_cell_complex/examples/Linear_cell_complex/map_3_iterators.cpp
+++ b/Linear_cell_complex/examples/Linear_cell_complex/map_3_iterators.cpp
@@ -24,7 +24,7 @@
 
 #define NUMBER_OF_LOOP 10
 
-typedef CGAL::Combinatorial_map_with_points<3> CMap_3;
+typedef CGAL::Linear_cell_complex<3> CMap_3;
 typedef CMap_3::Dart_handle          Dart_handle;
 
 int main(int narg, char** argv)
diff --git a/Linear_cell_complex/examples/Linear_cell_complex/map_3_subdivision.cpp b/Linear_cell_complex/examples/Linear_cell_complex/map_3_subdivision.cpp
index d3f06c6c4be..d448e572336 100644
--- a/Linear_cell_complex/examples/Linear_cell_complex/map_3_subdivision.cpp
+++ b/Linear_cell_complex/examples/Linear_cell_complex/map_3_subdivision.cpp
@@ -22,12 +22,12 @@
 #include <iostream>
 #include <fstream>
 
-typedef CGAL::Combinatorial_map_with_points<3>     LCC_3;
-typedef LCC_3::Dart_handle                         Dart_handle;
-typedef LCC_3::Vertex_attribute                    Vertex;
-typedef LCC_3::Point                               Point;
-typedef LCC_3::Vector                              Vector;
-typedef LCC_3::FT                                  FT;
+typedef CGAL::Linear_cell_complex<3> LCC_3;
+typedef LCC_3::Dart_handle           Dart_handle;
+typedef LCC_3::Vertex_attribute      Vertex;
+typedef LCC_3::Point                 Point;
+typedef LCC_3::Vector                Vector;
+typedef LCC_3::FT                    FT;
 
 #define PI 3.1415926535897932
 
@@ -177,20 +177,20 @@ void subdivide_map_3(LCC_3& m)
 Dart_handle make_iso_cuboid(LCC_3& lcc, const Point& basepoint, FT lg)
 {
 	return lcc.make_hexahedron(basepoint,
-                             LCC_3::Construct_translated_point()(basepoint,
-                                                                 LCC_3::Vector(lg,0,0)),
-                             LCC_3::Construct_translated_point()(basepoint,
-                                                                 LCC_3::Vector(lg,lg,0)),
-                             LCC_3::Construct_translated_point()(basepoint,
-                                                                 LCC_3::Vector(0,lg,0)),
-                             LCC_3::Construct_translated_point()(basepoint,
-                                                                 LCC_3::Vector(0,lg,lg)),
-                             LCC_3::Construct_translated_point()(basepoint,
-                                                                 LCC_3::Vector(0,0,lg)),
-                             LCC_3::Construct_translated_point()(basepoint,
-                                                                 LCC_3::Vector(lg,0,lg)),
-                             LCC_3::Construct_translated_point()(basepoint,
-                                                                 LCC_3::Vector(lg,lg,lg)));
+                             LCC_3::Traits::Construct_translated_point()(basepoint,
+                                                                 LCC_3::Traits::Vector(lg,0,0)),
+                             LCC_3::Traits::Construct_translated_point()(basepoint,
+                                                                 LCC_3::Traits::Vector(lg,lg,0)),
+                             LCC_3::Traits::Construct_translated_point()(basepoint,
+                                                                 LCC_3::Traits::Vector(0,lg,0)),
+                             LCC_3::Traits::Construct_translated_point()(basepoint,
+                                                                 LCC_3::Traits::Vector(0,lg,lg)),
+                             LCC_3::Traits::Construct_translated_point()(basepoint,
+                                                                 LCC_3::Traits::Vector(0,0,lg)),
+                             LCC_3::Traits::Construct_translated_point()(basepoint,
+                                                                 LCC_3::Traits::Vector(lg,0,lg)),
+                             LCC_3::Traits::Construct_translated_point()(basepoint,
+                                                                 LCC_3::Traits::Vector(lg,lg,lg)));
 }
 
 int main(int narg, char** argv)
diff --git a/Linear_cell_complex/examples/Linear_cell_complex/plane_graph_to_map_2.cpp b/Linear_cell_complex/examples/Linear_cell_complex/plane_graph_to_map_2.cpp
index 57d3c3f02fb..121c7f76551 100644
--- a/Linear_cell_complex/examples/Linear_cell_complex/plane_graph_to_map_2.cpp
+++ b/Linear_cell_complex/examples/Linear_cell_complex/plane_graph_to_map_2.cpp
@@ -23,9 +23,9 @@
 #include <fstream>
 #include <cstring>
 
-typedef CGAL::Combinatorial_map_with_points<2,2> Map_2;
-typedef Map_2::Dart_handle                       Dart_handle;
-typedef Map_2::Point                             Point;
+typedef CGAL::Linear_cell_complex<2,2> Map_2;
+typedef Map_2::Dart_handle             Dart_handle;
+typedef Map_2::Point                   Point;
 
 int main(int narg, char** argv)
 {
diff --git a/Linear_cell_complex/examples/Linear_cell_complex/polyhedron_clear.cpp b/Linear_cell_complex/examples/Linear_cell_complex/polyhedron_clear.cpp
index 30dba2e61e0..dc8fadfc2a6 100644
--- a/Linear_cell_complex/examples/Linear_cell_complex/polyhedron_clear.cpp
+++ b/Linear_cell_complex/examples/Linear_cell_complex/polyhedron_clear.cpp
@@ -67,9 +67,9 @@ void run(const char* fname,const char* info)
   bench<Poly_vector>(fname,"vector-based");  
 
   typedef CGAL::Linear_cell_complex_min_items<2> Items;
-  typedef CGAL::Combinatorial_map_with_points<2,3,
-																							CGAL::Linear_cell_complex_traits<3, Kernel>,
-																							Items> LCC;
+  typedef CGAL::Linear_cell_complex<2,3,
+                                    CGAL::Linear_cell_complex_traits<3, Kernel>,
+                                    Items> LCC;
   bench2<LCC>(fname,"Linear cell complex");
 }
 
diff --git a/Linear_cell_complex/examples/Linear_cell_complex/test-all b/Linear_cell_complex/examples/Linear_cell_complex/test-all
index 498c70a4ba5..186d45987b2 100755
--- a/Linear_cell_complex/examples/Linear_cell_complex/test-all
+++ b/Linear_cell_complex/examples/Linear_cell_complex/test-all
@@ -1,22 +1,11 @@
-cd debug; make; cd ..
+make;
 
-debug/map_3_with_points > res.txt 2>&1
-debug/map_5_with_points >> res.txt 2>&1
-debug/map_3_with_points_and_colored_vertices >> res.txt 2>&1
-debug/map_3_subdivision >> res.txt 2>&1
-debug/map_3_iterators data/aircraft.off  >> res.txt 2>&1
-debug/plane_graph_to_map_2 data/graph1.off >> res.txt 2>&1
-debug/voronoi_3 data/small_points >> res.txt 2>&1
-
-xxdiff res-valid.txt res.txt
-
-cd release; make; cd ..
-release/map_3_with_points > res.txt 2>&1
-release/map_5_with_points >> res.txt 2>&1
-release/map_3_with_points_and_colored_vertices >> res.txt 2>&1
-release/map_3_subdivision >> res.txt 2>&1
-release/map_3_iterators data/aircraft.off  >> res.txt 2>&1
-release/plane_graph_to_map_2 data/graph1.off >> res.txt 2>&1
-release/voronoi_3 data/small_points >> res.txt 2>&1
+./linear_cell_complex_3 > res.txt 2>&1
+./linear_cell_complex_4 >> res.txt 2>&1
+./linear_cell_complex_3_with_colored_vertices >> res.txt 2>&1
+./map_3_subdivision >> res.txt 2>&1
+./map_3_iterators data/aircraft.off  >> res.txt 2>&1
+./plane_graph_to_map_2 data/graph1.off >> res.txt 2>&1
+./voronoi_3 data/small_points >> res.txt 2>&1
 
 xxdiff res-valid.txt res.txt
diff --git a/Linear_cell_complex/examples/Linear_cell_complex/voronoi_3.cpp b/Linear_cell_complex/examples/Linear_cell_complex/voronoi_3.cpp
index 7206e15722d..0b578f3d4f4 100644
--- a/Linear_cell_complex/examples/Linear_cell_complex/voronoi_3.cpp
+++ b/Linear_cell_complex/examples/Linear_cell_complex/voronoi_3.cpp
@@ -26,9 +26,9 @@
 // #include "cgal_map_viewer_vtk.h"
 
 
-typedef CGAL::Combinatorial_map_with_points<3, 3> Map_3;
-typedef Map_3::Dart_handle                        Dart_handle;
-typedef Map_3::Point                              Point;
+typedef CGAL::Linear_cell_complex<3, 3> Map_3;
+typedef Map_3::Dart_handle              Dart_handle;
+typedef Map_3::Point                    Point;
 
 typedef CGAL::Delaunay_triangulation_3<Map_3::Traits> Triangulation;