diff --git a/Arrangement_on_surface_2/test/Arrangement_on_surface_2/test_sgm.cpp b/Arrangement_on_surface_2/test/Arrangement_on_surface_2/test_sgm.cpp
index 1e228a4b8f6..0b7889b4ed7 100644
--- a/Arrangement_on_surface_2/test/Arrangement_on_surface_2/test_sgm.cpp
+++ b/Arrangement_on_surface_2/test/Arrangement_on_surface_2/test_sgm.cpp
@@ -2,29 +2,41 @@
 
 // Testing the spherical gaussian map
 #include <iostream>
+
+#include <boost/iterator/iterator_facade.hpp>
+
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
 #include <CGAL/Polyhedron_3.h>
-#include <CGAL/Arr_spherical_gaussian_map_3/Arr_polyhedral_sgm_traits.h>
 #include <CGAL/Arr_spherical_gaussian_map_3/Arr_polyhedral_sgm.h>
 #include <CGAL/Arr_spherical_gaussian_map_3/Arr_polyhedral_sgm_polyhedron_3.h>
+#include <CGAL/convex_hull_3.h>
 
-typedef CGAL::Exact_predicates_exact_constructions_kernel       Kernel;
-typedef Kernel::Point_3                                         Point_3;
+using Kernel = CGAL::Exact_predicates_exact_constructions_kernel;
+using Point_3 = Kernel::Point_3;
 
 #if 1
-typedef CGAL::Arr_polyhedral_sgm_traits<Kernel, -1, 0>          Gm_traits;
+using Gm_traits = CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel, -1, 0>;
 #elif 0
-typedef CGAL::Arr_polyhedral_sgm_traits<Kernel, -8, 6>          Gm_traits;
+using Gm_traits = CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel, -8, 6>;
 #else
-typedef CGAL::Arr_polyhedral_sgm_traits<Kernel, -11, 7>         Gm_traits;
+using Gm_traits = CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel, -11, 7>;
 #endif
 
-typedef CGAL::Arr_polyhedral_sgm<Gm_traits>                     Gm;
-typedef CGAL::Arr_polyhedral_sgm_polyhedron_3<Gm, Kernel>       Gm_polyhedron;
-typedef CGAL::Arr_polyhedral_sgm_initializer<Gm, Gm_polyhedron> Gm_initializer;
+using Gm = CGAL::Arr_polyhedral_sgm<Gm_traits>;
+using Gm_polyhedron = CGAL::Arr_polyhedral_sgm_polyhedron_3<Gm, Kernel>;
+using Gm_initializer = CGAL::Arr_polyhedral_sgm_initializer<Gm, Gm_polyhedron>;
 
-int main()
-{
+struct Point_iterator :
+  boost::iterator_facade<Point_iterator, Point_3,
+                         std::forward_iterator_tag, Point_3> {
+  Point_iterator(Gm::Face_const_iterator it) : m_it(it) {}
+  void increment() { ++m_it; }
+  const Point_3& dereference() const { return m_it->point(); }
+  bool equal(Point_iterator const& o) const { return m_it == o.m_it; }
+  Gm::Face_const_iterator m_it;
+};
+
+int main() {
   // Construct the Gaussian map of a tetrahedron
   Point_3 points[] = {
     Point_3(1.0, 0.0, 0.0),
@@ -61,9 +73,9 @@ int main()
 
   Kernel::FT sw(16);
   Gm::Vertex_const_handle it;
-  for (it = gm.vertices_begin(); it != gm.vertices_end(); ++it) {
-    if (it->degree() < 3) continue;
-    Gm::Halfedge_around_vertex_const_circulator hec3(it->incident_halfedges());
+  for (auto vh : gm.vertex_handles()) {
+    if (vh->degree() < 3) continue;
+    Gm::Halfedge_around_vertex_const_circulator hec3(vh->incident_halfedges());
     Gm::Halfedge_around_vertex_const_circulator hec1 = hec3++;
     Gm::Halfedge_around_vertex_const_circulator hec2 = hec3++;
     std::cout << (*hec1).face()->point() << ", "
@@ -77,5 +89,13 @@ int main()
   }
   // std::cout << sw << std::endl;
   if ((3 * sw) != 1) return -1;
+
+  // The following tests the code Arr_polyhedral_sgm_polyhedron_3 that
+  // make the polyhedron a model of the FaceGraph concepts
+  Gm_polyhedron P;
+  Point_iterator begin(gm.faces_begin());
+  Point_iterator end(gm.faces_end());
+  CGAL::convex_hull_3(begin, end, P);
+
   return 0;
 }