diff --git a/Polyhedron_IO/examples/Polyhedron_IO/iv2off.cpp b/Polyhedron_IO/examples/Polyhedron_IO/iv2off.cpp
index d71ac7095a1..878f50fc818 100644
--- a/Polyhedron_IO/examples/Polyhedron_IO/iv2off.cpp
+++ b/Polyhedron_IO/examples/Polyhedron_IO/iv2off.cpp
@@ -2,7 +2,7 @@
 // The scanner triggers on Coordinate3, IndexedFaceSet, and IndexedLineSet
 // keywords. It does not recognize transformations nor groups.
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/IO/Verbose_ostream.h>
 #include <CGAL/IO/File_writer_OFF.h>
 #include <cstddef>
@@ -14,11 +14,11 @@
 
 using namespace std;
 
-typedef  CGAL::Cartesian<float>  Kernel;
-typedef  Kernel::Point_3         Point;
-typedef  list<Point>             Point_list;
-typedef  list<int>               Facet;
-typedef  list<Facet>             Facet_list;
+typedef  CGAL::Simple_cartesian<double>  Kernel;
+typedef  Kernel::Point_3                 Point;
+typedef  list<Point>                     Point_list;
+typedef  list<std::size_t>                       Facet;
+typedef  list<Facet>                     Facet_list;
 
 // Command line arguments
 // ======================
@@ -38,10 +38,10 @@ Facet_list  facets;
 // iv File Scanner
 // ===============
 void iv_file_scanner( istream& in) {
-    int     offset    = 0;    // offset for the Index....Set
-    char    c;                // one read character (comment, vertex, or facet)
-    char    str[2000];        // temporal storage for rest of identifier
-    int     blocks    = 0;    // Number of blocks found.
+  std::size_t offset    = 0;    // offset for the Index....Set
+    char      c;                // one read character (comment, vertex, or facet)
+    char      str[2000];        // temporal storage for rest of identifier
+    int       blocks    = 0;    // Number of blocks found.
 
     CGAL::Verbose_ostream vout( verbose);
     in >> str;
@@ -94,7 +94,7 @@ void iv_file_scanner( istream& in) {
                     vout << "\"IndexedFaceSet { coordIndex\" block found."
                          << endl;
                     // indices start here
-                    int face_offset = facets.size();
+                    std::size_t face_offset = facets.size();
                     in >> c;
                     CGAL_assertion( c == '[');
                     facets.push_back( Facet());
@@ -128,7 +128,7 @@ void iv_file_scanner( istream& in) {
                     vout << "\"IndexedLineSet { coordIndex\" block found."
                          << endl;
                     // indices start here
-                    int face_offset = facets.size();
+                    std::size_t face_offset = facets.size();
                     in >> c;
                     CGAL_assertion( c == '[');
                     facets.push_back( Facet());
diff --git a/Polyhedron_IO/examples/Polyhedron_IO/off2iv.cpp b/Polyhedron_IO/examples/Polyhedron_IO/off2iv.cpp
index d93500ec6fa..8ccc1409774 100644
--- a/Polyhedron_IO/examples/Polyhedron_IO/off2iv.cpp
+++ b/Polyhedron_IO/examples/Polyhedron_IO/off2iv.cpp
@@ -1,6 +1,5 @@
 // Convert from OFF format to OpenInventor (.iv) format.
 
-#include <CGAL/basic.h>
 #include <CGAL/IO/Verbose_ostream.h>
 #include <CGAL/IO/Inventor_ostream.h>
 #include <CGAL/IO/File_writer_inventor.h>
diff --git a/Polyhedron_IO/examples/Polyhedron_IO/off2off.cpp b/Polyhedron_IO/examples/Polyhedron_IO/off2off.cpp
index 877956f482d..a0a55752fa1 100644
--- a/Polyhedron_IO/examples/Polyhedron_IO/off2off.cpp
+++ b/Polyhedron_IO/examples/Polyhedron_IO/off2off.cpp
@@ -1,6 +1,5 @@
 // Copies a file in OFF format.
 
-#include <CGAL/basic.h>
 #include <CGAL/IO/Verbose_ostream.h>
 #include <CGAL/IO/File_writer_OFF.h>
 #include <CGAL/IO/generic_copy_OFF.h>
diff --git a/Polyhedron_IO/examples/Polyhedron_IO/off2vrml.cpp b/Polyhedron_IO/examples/Polyhedron_IO/off2vrml.cpp
index 1e3a49d79d0..23895ced7d7 100644
--- a/Polyhedron_IO/examples/Polyhedron_IO/off2vrml.cpp
+++ b/Polyhedron_IO/examples/Polyhedron_IO/off2vrml.cpp
@@ -1,6 +1,5 @@
 // Convert from OFF format to VRML (.wrl) 1.0 or 2.0 format.
 
-#include <CGAL/basic.h>
 #include <CGAL/IO/Verbose_ostream.h>
 #include <CGAL/IO/VRML_1_ostream.h>
 #include <CGAL/IO/VRML_2_ostream.h>
diff --git a/Polyhedron_IO/examples/Polyhedron_IO/off2wav.cpp b/Polyhedron_IO/examples/Polyhedron_IO/off2wav.cpp
index e0ad53b79df..3a5615fdae5 100644
--- a/Polyhedron_IO/examples/Polyhedron_IO/off2wav.cpp
+++ b/Polyhedron_IO/examples/Polyhedron_IO/off2wav.cpp
@@ -1,6 +1,5 @@
 // Convert from OFF format to Wavefront (.obj) format.
 
-#include <CGAL/basic.h>
 #include <CGAL/IO/Verbose_ostream.h>
 #include <CGAL/IO/File_writer_wavefront.h>
 #include <CGAL/IO/generic_copy_OFF.h>
diff --git a/Polyhedron_IO/examples/Polyhedron_IO/off_bbox.cpp b/Polyhedron_IO/examples/Polyhedron_IO/off_bbox.cpp
index 0bc281588c5..be4412cb53c 100644
--- a/Polyhedron_IO/examples/Polyhedron_IO/off_bbox.cpp
+++ b/Polyhedron_IO/examples/Polyhedron_IO/off_bbox.cpp
@@ -1,6 +1,5 @@
 // computes bbox of an OFF object.
 
-#include <CGAL/basic.h>
 #include <CGAL/Bbox_3.h>
 #include <CGAL/IO/Verbose_ostream.h>
 #include <CGAL/IO/File_scanner_OFF.h>
diff --git a/Polyhedron_IO/examples/Polyhedron_IO/off_glue.cpp b/Polyhedron_IO/examples/Polyhedron_IO/off_glue.cpp
index 457f4a4065c..d5a0a20e56f 100644
--- a/Polyhedron_IO/examples/Polyhedron_IO/off_glue.cpp
+++ b/Polyhedron_IO/examples/Polyhedron_IO/off_glue.cpp
@@ -1,6 +1,6 @@
 // Glue vertices of a polyhedron together that have equal coordinate values.
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/IO/Verbose_ostream.h>
 #include <CGAL/IO/File_scanner_OFF.h>
 #include <CGAL/IO/File_writer_OFF.h>
@@ -14,9 +14,9 @@
 
 using namespace std;
 
-typedef  CGAL::Cartesian<float>  Kernel;
-typedef  Kernel::Point_3         Point;
-typedef  Kernel::Vector_3        Vector;
+typedef  CGAL::Simple_cartesian<double>  Kernel;
+typedef  Kernel::Point_3                 Point;
+typedef  Kernel::Vector_3                Vector;
 struct   Vertex {
     Point   point;
     Vector  normal;
@@ -179,11 +179,11 @@ int main( int argc, char **argv) {
     // Copy facets and translate vertex indices.
     writer.write_facet_header();
     for ( i = 0; i < scanner.size_of_facets(); i++) {
-        int no;  // number of vertices of a facet.
+      std::size_t no;  // number of vertices of a facet.
         scanner.scan_facet( no, i);
         writer.write_facet_begin( no);
         for ( int j = 0; j < no; j++) {
-            int index;
+          std::size_t index;
             scanner.scan_facet_vertex_index( index, i);
             writer.write_facet_vertex_index(  vertices[index].index);
         }
diff --git a/Polyhedron_IO/examples/Polyhedron_IO/off_transform.cpp b/Polyhedron_IO/examples/Polyhedron_IO/off_transform.cpp
index f66fe32f616..8993a93a392 100644
--- a/Polyhedron_IO/examples/Polyhedron_IO/off_transform.cpp
+++ b/Polyhedron_IO/examples/Polyhedron_IO/off_transform.cpp
@@ -1,6 +1,6 @@
 // Applies translation and scaling to an OFF object.
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/IO/Verbose_ostream.h>
 #include <CGAL/IO/File_scanner_OFF.h>
 #include <CGAL/IO/File_writer_OFF.h>
@@ -12,9 +12,9 @@
 
 using namespace std;
 
-typedef  CGAL::Cartesian<float>  Kernel;
-typedef  Kernel::Point_3         Point;
-typedef  Kernel::Vector_3        Vector;
+typedef  CGAL::Simple_cartesian<double>  Kernel;
+typedef  Kernel::Point_3                 Point;
+typedef  Kernel::Vector_3                Vector;
 
 bool    verbose      = false;
 bool    binary       = false;
diff --git a/Polyhedron_IO/examples/Polyhedron_IO/polyhedron_copy.cpp b/Polyhedron_IO/examples/Polyhedron_IO/polyhedron_copy.cpp
index 31d3c3d1e56..b192f224fe5 100644
--- a/Polyhedron_IO/examples/Polyhedron_IO/polyhedron_copy.cpp
+++ b/Polyhedron_IO/examples/Polyhedron_IO/polyhedron_copy.cpp
@@ -1,6 +1,6 @@
 // Copies a CGAL::Polyhedron_3 from OFF format to OFF format.
 
-#include <CGAL/Cartesian.h>
+#include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/IO/Polyhedron_iostream.h>
 #include <CGAL/IO/Verbose_ostream.h>
@@ -12,8 +12,8 @@
 
 using namespace std;
 
-typedef CGAL::Cartesian<double>     Kernel;
-typedef CGAL::Polyhedron_3<Kernel>  Polyhedron;
+typedef CGAL::Simple_cartesian<double>     Kernel;
+typedef CGAL::Polyhedron_3<Kernel>         Polyhedron;
 
 bool  verbose   = false;
 bool  binary    = false;