diff --git a/Triangulation_3/test/Triangulation_3/test_segment_simplex_traverser_3.cpp b/Triangulation_3/test/Triangulation_3/test_segment_simplex_traverser_3.cpp
index 7e764052706..a6b53e4cf5e 100644
--- a/Triangulation_3/test/Triangulation_3/test_segment_simplex_traverser_3.cpp
+++ b/Triangulation_3/test/Triangulation_3/test_segment_simplex_traverser_3.cpp
@@ -34,6 +34,8 @@ typedef DT::Vertex_handle                      Vertex_handle;
 typedef DT::Simplex                            Simplex;
 typedef DT::Segment_simplex_iterator           Segment_simplex_iterator;
 
+#include "test_triangulation_simplex_3_debug.h"
+
 // a function to insert without spatial sorting
 template <typename Point_it>
 void insert(DT& dt, Point_it first, Point_it end) {
@@ -41,62 +43,6 @@ void insert(DT& dt, Point_it first, Point_it end) {
     dt.insert(*first);
   }
 }
-auto display_vert(Vertex_handle v) {
-  std::stringstream os;
-  os.precision(17);
-  if(v->time_stamp() == 0) {
-    os << "inf";
-  } else {
-    os << '#' << v->time_stamp() << "=(" << v->point() << ")";
-  }
-  return os.str();
-};
-
-struct Debug_simplex {
-  Simplex simplex;
-
-  template<typename CharT, typename Traits>
-  friend
-  std::basic_ostream<CharT, Traits>&
-  operator<<(std::basic_ostream<CharT, Traits>& os, const Debug_simplex& d) {
-    auto&& simplex = d.simplex;
-    switch(simplex.dimension()) {
-      case 0: {
-        os << "- vertex " << display_vert(static_cast<Vertex_handle>(simplex));
-        break;
-      }
-      case 1: {
-        const auto [c, index1, index2] = static_cast<Edge>(simplex);
-        os << "- edge "
-           << display_vert(c->vertex(index1)) << " - "
-           << display_vert(c->vertex(index2));
-        break;
-      }
-      case 2: {
-        const auto [c, index] = static_cast<Facet>(simplex);
-        os << "- facet "
-           << display_vert(c->vertex(DT::vertex_triple_index(index, 0))) << " - "
-           << display_vert(c->vertex(DT::vertex_triple_index(index, 1))) << " - "
-           << display_vert(c->vertex(DT::vertex_triple_index(index, 2)));
-        break;
-      }
-      case 3: {
-        const auto c = static_cast<Cell_handle>(simplex);
-        os << "- cell "
-           << display_vert(c->vertex(0)) << " - "
-           << display_vert(c->vertex(1)) << " - "
-           << display_vert(c->vertex(2)) << " - "
-           << display_vert(c->vertex(3));
-        break;
-      }
-      default: CGAL_assume(false);
-    }
-    return os;
-  };
-};
-auto debug_simplex(Simplex simplex) {
-  return Debug_simplex{simplex};
-}
 
 static const std::vector<Point_3> bbox_points =
 {
diff --git a/Triangulation_3/test/Triangulation_3/test_simplex_iterator_3.cpp b/Triangulation_3/test/Triangulation_3/test_simplex_iterator_3.cpp
index 048581c0d90..506fd81022c 100644
--- a/Triangulation_3/test/Triangulation_3/test_simplex_iterator_3.cpp
+++ b/Triangulation_3/test/Triangulation_3/test_simplex_iterator_3.cpp
@@ -1,5 +1,7 @@
+// #define CGAL_DEBUG_TRIANGULATION_SEGMENT_TRAVERSER_3 1
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
 #include <CGAL/Delaunay_triangulation_3.h>
+#include <CGAL/Base_with_time_stamp.h>
 
 #include <assert.h>
 #include <iostream>
@@ -17,14 +19,20 @@ typedef Kernel::Vector_3                                      Vector_3;
 typedef Kernel::Segment_3                                     Segment_3;
 
 // Define the structure.
-typedef CGAL::Delaunay_triangulation_3< Kernel >    DT;
+typedef CGAL::Base_with_time_stamp<CGAL::Triangulation_vertex_base_3<Kernel>> Vb;
+typedef CGAL::Delaunay_triangulation_cell_base_3<Kernel> Cb;
+typedef CGAL::Triangulation_data_structure_3<Vb, Cb>     Tds;
+typedef CGAL::Delaunay_triangulation_3< Kernel, Tds >    DT;
 
 typedef DT::Vertex_handle                           Vertex_handle;
 typedef DT::Cell_handle                             Cell_handle;
 typedef DT::Edge                                    Edge;
 typedef DT::Facet                                   Facet;
+typedef DT::Simplex                                 Simplex;
 typedef DT::Segment_simplex_iterator                Segment_simplex_iterator;
 
+#include "test_triangulation_simplex_3_debug.h"
+
 void test_vertex_edge_vertex(const DT& dt, const std::size_t& nb_tests)
 {
   std::cout << "* test_vertex_edge_vertex *" << std::endl;
@@ -299,8 +307,8 @@ void test_triangulation_on_a_grid()
     unsigned int nb_facets = 0, nb_edges = 0, nb_vertex = 0;
     for (; st != st.end(); ++st)
     {
-      std::cout << st->dimension() << " ";
-      std::cout.flush();
+      std::cerr << st->dimension() << " ";
+      std::cerr << debug_simplex(*st) <<'\n';
       if (st->dimension() == 3)
       {
         if (dt.is_infinite(Cell_handle(*st))) ++inf;
diff --git a/Triangulation_3/test/Triangulation_3/test_triangulation_simplex_3_debug.h b/Triangulation_3/test/Triangulation_3/test_triangulation_simplex_3_debug.h
new file mode 100644
index 00000000000..5ea79279b1c
--- /dev/null
+++ b/Triangulation_3/test/Triangulation_3/test_triangulation_simplex_3_debug.h
@@ -0,0 +1,68 @@
+template <typename Vertex_handle>
+auto display_vert(Vertex_handle v) {
+  std::stringstream os;
+  os.precision(17);
+  if(v->time_stamp() == 0) {
+    os << "inf";
+  } else {
+    os << '#' << v->time_stamp() << "=(" << v->point() << ")";
+  }
+  return os.str();
+};
+
+template <typename DT>
+struct Debug_simplex {
+  using Cell_handle = typename DT::Cell_handle;
+  using Edge = typename DT::Edge;
+  using Facet = typename DT::Facet;
+  using Vertex_handle = typename DT::Vertex_handle;
+  using Simplex = typename DT::Simplex;
+
+  Simplex simplex;
+
+  template<typename Dt, typename CharT, typename Traits>
+  friend
+  std::basic_ostream<CharT, Traits>&
+  operator<<(std::basic_ostream<CharT, Traits>& os, const Debug_simplex<Dt>& d) {
+    auto&& simplex = d.simplex;
+    switch(simplex.dimension()) {
+      case 0: {
+        os << "- vertex " << display_vert(static_cast<Vertex_handle>(simplex));
+        break;
+      }
+      case 1: {
+        const auto [c, index1, index2] = static_cast<Edge>(simplex);
+        os << "- edge "
+           << display_vert(c->vertex(index1)) << " - "
+           << display_vert(c->vertex(index2));
+        break;
+      }
+      case 2: {
+        const auto [c, index] = static_cast<Facet>(simplex);
+        os << "- facet "
+           << display_vert(c->vertex(DT::vertex_triple_index(index, 0))) << " - "
+           << display_vert(c->vertex(DT::vertex_triple_index(index, 1))) << " - "
+           << display_vert(c->vertex(DT::vertex_triple_index(index, 2)));
+        break;
+      }
+      case 3: {
+        const auto c = static_cast<Cell_handle>(simplex);
+        os << "- cell "
+           << display_vert(c->vertex(0)) << " - "
+           << display_vert(c->vertex(1)) << " - "
+           << display_vert(c->vertex(2)) << " - "
+           << display_vert(c->vertex(3));
+        break;
+      }
+      default: CGAL_assume(false);
+    }
+    return os;
+  };
+};
+
+#include <CGAL/Triangulation_simplex_3.h>
+
+template <typename Triangulation>
+auto debug_simplex(CGAL::Triangulation_simplex_3<Triangulation> simplex) {
+  return Debug_simplex<Triangulation>{simplex};
+}