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diff --git a/Alpha_shapes_3/examples/Alpha_shapes_3/ex_periodic_alpha_shapes_3.cpp b/Alpha_shapes_3/examples/Alpha_shapes_3/ex_periodic_alpha_shapes_3.cpp
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+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Periodic_3_triangulation_traits_3.h>
+#include <CGAL/Periodic_3_Delaunay_triangulation_3.h>
+#include <CGAL/Alpha_shape_3.h>
+
+#include <CGAL/Random.h>
+#include <CGAL/point_generators_3.h>
+
+// Traits
+typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
+typedef CGAL::Periodic_3_triangulation_traits_3<K> PK;
+
+// Vertex type
+typedef CGAL::Periodic_3_triangulation_ds_vertex_base_3<> DsVb;
+typedef CGAL::Triangulation_vertex_base_3<PK,DsVb> Vb;
+typedef CGAL::Alpha_shape_vertex_base_3<PK,Vb> AsVb;
+// Cell type
+typedef CGAL::Periodic_3_triangulation_ds_cell_base_3<> DsCb;
+typedef CGAL::Triangulation_cell_base_3<PK,DsCb> Cb;
+typedef CGAL::Alpha_shape_cell_base_3<PK,Cb> AsCb;
+
+typedef CGAL::Triangulation_data_structure_3<AsVb,AsCb> Tds;
+typedef CGAL::Periodic_3_Delaunay_triangulation_3<PK,Tds> P3DT3;
+typedef CGAL::Alpha_shape_3<P3DT3>  Alpha_shape_3;
+
+typedef PK::Point_3                                 Point;
+
+int main()
+{
+  typedef CGAL::Creator_uniform_3<double, Point> Creator;
+  CGAL::Random random(7);
+  CGAL::Random_points_in_cube_3<Point, Creator> in_cube(1, random);
+  std::vector<Point> pts;
+
+  // Generating 1000 random points
+  for (int i=0 ; i < 1000 ; i++) {
+    Point p = *in_cube++;
+    pts.push_back(p);
+  }
+
+  // Define the periodic cube
+  P3DT3 pdt(PK::Iso_cuboid_3(-1,-1,-1,1,1,1));
+  // Heuristic for inserting large point sets (if pts is reasonably large)
+  pdt.insert(pts.begin(), pts.end(), true);
+  // As pdt won't be modified anymore switch to 1-sheeted cover if possible
+  if (pdt.is_triangulation_in_1_sheet()) pdt.convert_to_1_sheeted_covering();
+  std::cout << "Periodic Delaunay computed." << std::endl;
+
+  // compute alpha shape
+  Alpha_shape_3 as(pdt);
+  std::cout << "Alpha shape computed in REGULARIZED mode by default."
+	    << std::endl;
+
+   // find optimal alpha values
+  Alpha_shape_3::NT alpha_solid = as.find_alpha_solid();
+  Alpha_shape_3::Alpha_iterator opt = as.find_optimal_alpha(1);
+  std::cout << "Smallest alpha value to get a solid through data points is "
+	    << alpha_solid << std::endl;
+  std::cout << "Optimal alpha value to get one connected component is "
+	    <<  *opt    << std::endl;
+  as.set_alpha(*opt);
+  assert(as.number_of_solid_components() == 1);
+  return 0;
+}