diff --git a/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/data/data1.dt.cin b/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/data/data1.dt.cin
index c1c3fe53450..30765637fa5 100644
--- a/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/data/data1.dt.cin
+++ b/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/data/data1.dt.cin
@@ -1,3 +1,20 @@
-0.6 0.2
-0.4 0.4
-0.2 0.8
+0.192592592592593	0.037037037037037
+0.17037037037037	0.177777777777778
+0.451851851851852	0.111111111111111
+0.274074074074074	0.37037037037037
+0.133333333333333	0.592592592592593
+0.037037037037037	0.688888888888889
+0.177777777777778	0.844444444444444
+0.288888888888889	0.674074074074074
+0.318518518518519	0.925925925925926
+0.540740740740741	0.844444444444444
+0.637037037037037	0.703703703703704
+0.511111111111111	0.496296296296296
+0.725925925925926	0.237037037037037
+0.933333333333333	0.22962962962963
+0.733333333333333	0.511111111111111
+0.925925925925926	0.459259259259259
+0.866666666666667	0.777777777777778
+0.77037037037037	0.925925925925926
+0.881481481481482	0.977777777777778
+0.990000000000000       0.911111111111111
diff --git a/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/draw_periodic_2_triangulation_2.cpp b/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/draw_periodic_2_triangulation_2.cpp
index c8f6aeb27f7..676ca27746d 100644
--- a/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/draw_periodic_2_triangulation_2.cpp
+++ b/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/draw_periodic_2_triangulation_2.cpp
@@ -1,12 +1,12 @@
-#include <CGAL/Periodic_2_triangulation_2.h>
-#include <CGAL/Periodic_2_triangulation_traits_2.h>
+#include <CGAL/Periodic_2_Delaunay_triangulation_2.h>
+#include <CGAL/Periodic_2_Delaunay_triangulation_traits_2.h>
 #include <CGAL/draw_periodic_2_triangulation_2.h>
 
 #include<fstream>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
-typedef CGAL::Periodic_2_triangulation_traits_2<K>          GT;
-typedef CGAL::Periodic_2_triangulation_2<GT>                PDT;
+typedef CGAL::Periodic_2_Delaunay_triangulation_traits_2<K> GT;
+typedef CGAL::Periodic_2_Delaunay_triangulation_2<GT>       PDT;
 
 typedef PDT::Point                                          Point;
 
@@ -24,6 +24,11 @@ int main(int argc, char* argv[])
   }
   assert(T.is_valid());
 
+  if( T.is_triangulation_in_1_sheet())
+    T.convert_to_9_sheeted_covering();
+
   // Draw the periodic triangulation
   CGAL::draw(T);
+
+  return EXIT_SUCCESS;
 }
diff --git a/Periodic_2_triangulation_2/include/CGAL/draw_periodic_2_triangulation_2.h b/Periodic_2_triangulation_2/include/CGAL/draw_periodic_2_triangulation_2.h
index 60c63b513dc..a20f4d21f50 100644
--- a/Periodic_2_triangulation_2/include/CGAL/draw_periodic_2_triangulation_2.h
+++ b/Periodic_2_triangulation_2/include/CGAL/draw_periodic_2_triangulation_2.h
@@ -120,6 +120,8 @@ protected:
     add_point_in_face(t[2]);
     face_end();
 
+    // Display the edges of the faces as segments with a
+    // light gray color for better visualization
     add_segment(t[0], t[1], CGAL::Color(207, 213, 211));
     add_segment(t[1], t[2], CGAL::Color(207, 213, 211));
     add_segment(t[2], t[0], CGAL::Color(207, 213, 211));