diff --git a/SMDS_3/doc/SMDS_3/examples.txt b/SMDS_3/doc/SMDS_3/examples.txt
index fe33a6e5c64..df44fa577ec 100644
--- a/SMDS_3/doc/SMDS_3/examples.txt
+++ b/SMDS_3/doc/SMDS_3/examples.txt
@@ -1,4 +1,5 @@
 /*!
 \example SMDS_3/c3t3_example.cpp
+\example SMDS_3/c3t3_complete_example.cpp
 \example SMDS_3/tetrahedron_soup_to_c3t3_example.cpp
 */
diff --git a/SMDS_3/examples/SMDS_3/CMakeLists.txt b/SMDS_3/examples/SMDS_3/CMakeLists.txt
index 77d7ba6b6a8..d3485b91965 100644
--- a/SMDS_3/examples/SMDS_3/CMakeLists.txt
+++ b/SMDS_3/examples/SMDS_3/CMakeLists.txt
@@ -9,4 +9,5 @@ project(SMDS_3_Examples)
 find_package(CGAL REQUIRED)
 
 create_single_source_cgal_program("c3t3_example.cpp")
+create_single_source_cgal_program("c3t3_complete_example.cpp")
 create_single_source_cgal_program("tetrahedron_soup_to_c3t3_example.cpp")
diff --git a/SMDS_3/examples/SMDS_3/c3t3_complete_example.cpp b/SMDS_3/examples/SMDS_3/c3t3_complete_example.cpp
new file mode 100644
index 00000000000..5ebb5cc3e35
--- /dev/null
+++ b/SMDS_3/examples/SMDS_3/c3t3_complete_example.cpp
@@ -0,0 +1,67 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+#include <CGAL/Triangulation_3.h>
+#include <CGAL/Triangulation_data_structure_3.h>
+#include <CGAL/Simplicial_mesh_cell_base_3.h>
+#include <CGAL/Simplicial_mesh_vertex_base_3.h>
+#include <CGAL/Mesh_complex_3_in_triangulation_3.h>
+
+#include <CGAL/tetrahedral_remeshing.h>
+
+#include <CGAL/tags.h>
+
+#include <CGAL/IO/File_medit.h>
+#include <fstream>
+
+
+using K = CGAL::Exact_predicates_inexact_constructions_kernel;
+
+using Subdomain_index = int;
+using Surface_patch_index = unsigned char;
+using Curve_index = char;
+using Corner_index = short;
+
+using Cb = CGAL::Simplicial_mesh_cell_base_3<K, Subdomain_index, Surface_patch_index>;
+using Vb = CGAL::Simplicial_mesh_vertex_base_3<K, Subdomain_index, Surface_patch_index,
+                                                  Curve_index, Corner_index>;
+
+using Tds = CGAL::Triangulation_data_structure_3<Vb, Cb, CGAL::Sequential_tag>;
+using Triangulation = CGAL::Triangulation_3<K, Tds>;
+
+using C3t3 = CGAL::Mesh_complex_3_in_triangulation_3<Triangulation>;
+
+
+int main(int argc, char* argv[])
+{
+  std::cout.precision(17);
+  std::cerr.precision(17);
+
+  std::string filename = (argc > 1) ? std::string(argv[1])
+                       : CGAL::data_file_path("meshes/elephant.mesh");
+
+  Triangulation tr;
+
+  std::ifstream is(filename, std::ios_base::in);
+  if(!CGAL::IO::read_MEDIT(is, tr))
+  {
+    std::cerr << "Failed to read" << std::endl;
+    return EXIT_FAILURE;
+  }
+
+  // [call a remeshing algorithm]
+
+  std::ofstream os("after_remeshing.mesh");
+  CGAL::IO::write_MEDIT(os, tr, CGAL::parameters::all_vertices(true));
+  os.close();
+
+  Triangulation tr2;
+  std::ifstream is2("after_remeshing.mesh");
+  if(!CGAL::IO::read_MEDIT(is2, tr2))
+  {
+    std::cerr << "Failed to read (#2)" << std::endl;
+    return EXIT_FAILURE;
+  }
+
+  std::cout << "Done" << std::endl;
+  return EXIT_SUCCESS;
+}
diff --git a/SMDS_3/examples/SMDS_3/c3t3_example.cpp b/SMDS_3/examples/SMDS_3/c3t3_example.cpp
index 5ebb5cc3e35..6a881fe5301 100644
--- a/SMDS_3/examples/SMDS_3/c3t3_example.cpp
+++ b/SMDS_3/examples/SMDS_3/c3t3_example.cpp
@@ -1,36 +1,16 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 
-#include <CGAL/Triangulation_3.h>
-#include <CGAL/Triangulation_data_structure_3.h>
-#include <CGAL/Simplicial_mesh_cell_base_3.h>
-#include <CGAL/Simplicial_mesh_vertex_base_3.h>
+#include <CGAL/Simplicial_mesh_triangulation_3.h>
 #include <CGAL/Mesh_complex_3_in_triangulation_3.h>
 
-#include <CGAL/tetrahedral_remeshing.h>
-
-#include <CGAL/tags.h>
-
 #include <CGAL/IO/File_medit.h>
 #include <fstream>
 
-
 using K = CGAL::Exact_predicates_inexact_constructions_kernel;
 
-using Subdomain_index = int;
-using Surface_patch_index = unsigned char;
-using Curve_index = char;
-using Corner_index = short;
-
-using Cb = CGAL::Simplicial_mesh_cell_base_3<K, Subdomain_index, Surface_patch_index>;
-using Vb = CGAL::Simplicial_mesh_vertex_base_3<K, Subdomain_index, Surface_patch_index,
-                                                  Curve_index, Corner_index>;
-
-using Tds = CGAL::Triangulation_data_structure_3<Vb, Cb, CGAL::Sequential_tag>;
-using Triangulation = CGAL::Triangulation_3<K, Tds>;
-
+using Triangulation = CGAL::Simplicial_mesh_triangulation_3<K>;
 using C3t3 = CGAL::Mesh_complex_3_in_triangulation_3<Triangulation>;
 
-
 int main(int argc, char* argv[])
 {
   std::cout.precision(17);
@@ -48,20 +28,12 @@ int main(int argc, char* argv[])
     return EXIT_FAILURE;
   }
 
-  // [call a remeshing algorithm]
+  C3t3 c3t3;
+  c3t3.triangulation() = tr;
 
-  std::ofstream os("after_remeshing.mesh");
+  std::ofstream os("out.mesh");
   CGAL::IO::write_MEDIT(os, tr, CGAL::parameters::all_vertices(true));
   os.close();
 
-  Triangulation tr2;
-  std::ifstream is2("after_remeshing.mesh");
-  if(!CGAL::IO::read_MEDIT(is2, tr2))
-  {
-    std::cerr << "Failed to read (#2)" << std::endl;
-    return EXIT_FAILURE;
-  }
-
-  std::cout << "Done" << std::endl;
   return EXIT_SUCCESS;
 }
diff --git a/SMDS_3/include/CGAL/Simplicial_mesh_triangulation_3.h b/SMDS_3/include/CGAL/Simplicial_mesh_triangulation_3.h
new file mode 100644
index 00000000000..918d70cb37f
--- /dev/null
+++ b/SMDS_3/include/CGAL/Simplicial_mesh_triangulation_3.h
@@ -0,0 +1,51 @@
+// Copyright (c) 2006-2007  INRIA Sophia-Antipolis (France).
+// Copyright (c) 2008,2011 GeometryFactory Sarl (France)
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
+//
+// Author(s)     : Laurent Rineau, Stephane Tayeb, Andreas Fabri, Jane Tournois
+
+#ifndef CGAL_SIMPLICIAL_MESH_TRIANGULATION_3_H
+#define CGAL_SIMPLICIAL_MESH_TRIANGULATION_3_H
+
+#include <CGAL/license/SMDS_3.h>
+
+#include <CGAL/Simplicial_mesh_vertex_base_3.h>
+#include <CGAL/Simplicial_mesh_cell_base_3.h>
+#include <CGAL/Triangulation_data_structure_3.h>
+#include <CGAL/Triangulation_3.h>
+
+namespace CGAL
+{
+  /**
+  *\ingroup PkgSMDS3Classes
+  * `Simplicial_mesh_triangulation_3`
+  * @todo
+  */
+  template<typename K,
+           typename SubdomainIndex = int,
+           typename SurfacePatchIndex = int,
+           typename CurveIndex = int,
+           typename CornerIndex = int>
+  using Simplicial_mesh_triangulation_3 =
+      CGAL::Triangulation_3<K,
+        CGAL::Triangulation_data_structure_3<
+          CGAL::Simplicial_mesh_vertex_base_3<K,
+                                              SubdomainIndex,
+                                              SurfacePatchIndex,
+                                              CurveIndex,
+                                              CornerIndex>,
+          CGAL::Simplicial_mesh_cell_base_3<K, SubdomainIndex, SurfacePatchIndex>,
+          CGAL::Sequential_tag
+        >
+      >;
+};
+
+#endif // CGAL_SIMPLICIAL_MESH_TRIANGULATION_3_H
+
+