diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/triangulate_faces_test.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/triangulate_faces_test.cpp
index 5f239c7dfaa..61546684005 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/triangulate_faces_test.cpp
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/triangulate_faces_test.cpp
@@ -1,13 +1,14 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
-
 #include <CGAL/Surface_mesh.h>
 
+#include <CGAL/Polygon_mesh_processing/triangulate_faces.h>
+
 #include <CGAL/boost/graph/copy_face_graph.h>
 #include <CGAL/boost/graph/Dual.h>
 #include <CGAL/boost/graph/named_params_helper.h>
 #include <CGAL/centroid.h>
-#include <CGAL/Polygon_mesh_processing/triangulate_faces.h>
+#include <CGAL/Polygon_mesh_processing/polygon_mesh_to_polygon_soup.h>
 
 #include <boost/graph/filtered_graph.hpp>
 
@@ -117,21 +118,17 @@ test_triangulate_face()
     return false;
   }
 
-  unsigned int nb = 0;
   for(typename boost::graph_traits<Surface_mesh>::face_descriptor fit : faces(mesh))
   {
-    if (nb > 4)
-      break;
-    else if (next(next(halfedge(fit, mesh), mesh), mesh)
-             !=   prev(halfedge(fit, mesh), mesh))
+    if (next(next(halfedge(fit, mesh), mesh), mesh) !=   prev(halfedge(fit, mesh), mesh))
     {
-      if(CGAL::Polygon_mesh_processing::triangulate_face(fit, mesh))
-        ++nb;
-      else
+      if(!CGAL::Polygon_mesh_processing::triangulate_face(fit, mesh))
         assert(false);
     }
   }
 
+  assert(CGAL::is_triangle_mesh(mesh));
+
   return true;
 }
 
@@ -156,6 +153,9 @@ test_triangulate_triangle_face()
     if(!CGAL::Polygon_mesh_processing::triangulate_face(fit, mesh, CGAL::parameters::geom_traits(K())))
       assert(false);
   }
+
+  assert(CGAL::is_triangle_mesh(mesh));
+
   return true;
 }
 
@@ -238,9 +238,54 @@ test_dual_with_various_faces()
     if(!CGAL::Polygon_mesh_processing::triangulate_face(fit, sm_dual))
       assert(false);
   }
+
+  assert(CGAL::is_triangle_mesh(sm_dual));
+
   return true;
 }
 
+template <typename K>
+bool
+test_triangulate_soup()
+{
+  typedef typename K::Point_3                    Point;
+  typedef CGAL::Surface_mesh<Point>          Surface_mesh;
+
+  Surface_mesh mesh;
+  std::ifstream input(CGAL::data_file_path("meshes/elephant.off"));
+
+  if (!input || !(input >> mesh) || mesh.is_empty())
+  {
+    std::cerr << "Not a valid off file." << std::endl;
+    return false;
+  }
+
+  typedef typename boost::property_map<Surface_mesh, boost::vertex_point_t>::type Pmap;
+  Pmap vpmap = get_property_map(boost::vertex_point, mesh);
+
+  CGAL::Dual<Surface_mesh> dual(mesh);
+  // copy dual to a sm
+  Surface_mesh sm_dual;
+  CGAL::copy_face_graph(dual, sm_dual,
+                        CGAL::parameters::vertex_point_map(
+                          Dual_vpm<Surface_mesh, Point, Pmap>(mesh, vpmap)));
+
+  std::vector<Point> points;
+  std::vector<std::vector<std::size_t> > polygons;
+  CGAL::Polygon_mesh_processing::polygon_mesh_to_polygon_soup(sm_dual, points, polygons);
+
+  bool success = CGAL::Polygon_mesh_processing::triangulate_polygons(points, polygons);
+  for(std::size_t i = 0; i < polygons.size(); ++i)
+  {
+    assert(polygons[i].size() == 3);
+  }
+
+  // For compilation
+  success = CGAL::Polygon_mesh_processing::triangulate_polygons(points, polygons, CGAL::parameters::geom_traits(K()));
+
+  return success;
+}
+
 int main()
 {
   assert(test_triangulate_faces<Epic>());
@@ -249,6 +294,7 @@ int main()
   assert(test_triangulate_face<Epic>());
   assert(test_triangulate_triangle_face<Epic>());
   assert(test_dual_with_various_faces<Epic>());
+  assert(test_triangulate_soup<Epic>());
 
   assert(test_triangulate_faces<Epec>());
   assert(test_triangulate_faces_with_named_parameters<Epec>());
@@ -256,6 +302,8 @@ int main()
   assert(test_triangulate_face<Epec>());
   assert(test_triangulate_triangle_face<Epec>());
   assert(test_dual_with_various_faces<Epec>());
+  assert(test_triangulate_soup<Epec>());
 
+  std::cout << "Done" << std::endl;
   return EXIT_SUCCESS;
 }