diff --git a/Triangulation_on_sphere_2/include/CGAL/Triangulation_on_sphere_face_base_2.h b/Triangulation_on_sphere_2/include/CGAL/Triangulation_on_sphere_face_base_2.h
new file mode 100644
index 00000000000..405761fc3c4
--- /dev/null
+++ b/Triangulation_on_sphere_2/include/CGAL/Triangulation_on_sphere_face_base_2.h
@@ -0,0 +1,84 @@
+// Copyright (c) 1997, 2012, 2019 INRIA Sophia-Antipolis (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+// You can redistribute it and/or modify it under the terms of the GNU
+// General Public License as published by the Free Software Foundation,
+// either version 3 of the Licenxse, or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0+
+//
+// Author(s)     : Mariette Yvinec, Claudia Werner
+
+#ifndef CGAL_Triangulation_on_sphere_face_base_2_H
+#define CGAL_Triangulation_on_sphere_face_base_2_H
+
+#include <CGAL/Triangulation_ds_face_base_2.h>
+
+namespace CGAL {
+
+template <typename Gt,
+          typename Fb = Triangulation_ds_face_base_2<> >
+class Triangulation_on_sphere_face_base_2
+    : public Fb
+{
+public:
+  typedef Gt                                                  Geom_traits;
+  typedef typename Fb::Vertex_handle                          Vertex_handle;
+  typedef typename Fb::Face_handle                            Face_handle;
+
+  template < typename TDS2 >
+  struct Rebind_TDS {
+    typedef typename Fb::template Rebind_TDS<TDS2>::Other     Fb2;
+    typedef Triangulation_on_sphere_face_base_2<Gt, Fb2>      Other;
+  };
+
+public:
+  void set_in_conflict_flag(unsigned char f) { _in_conflict_flag = f; }
+  unsigned char get_in_conflict_flag() const { return _in_conflict_flag; }
+
+public:
+  Triangulation_on_sphere_face_base_2()
+    : Fb(), _ghost(false)
+  {
+    set_in_conflict_flag(0);
+  }
+
+  Triangulation_on_sphere_face_base_2(Vertex_handle v0,
+                                      Vertex_handle v1,
+                                      Vertex_handle v2)
+    : Fb(v0, v1, v2), _ghost(false)
+  {
+    set_in_conflict_flag(0);
+  }
+
+  Triangulation_on_sphere_face_base_2(Vertex_handle v0,
+                                      Vertex_handle v1,
+                                      Vertex_handle v2,
+                                      Face_handle n0,
+                                      Face_handle n1,
+                                      Face_handle n2)
+    : Fb(v0, v1, v2, n0, n1, n2), _ghost(false)
+  {
+    set_in_conflict_flag(0);
+  }
+
+  bool is_ghost() const { return _ghost; }
+  bool& ghost() { return _ghost; }
+
+protected:
+  bool _ghost;
+  unsigned char _in_conflict_flag;
+};
+
+} // namespace CGAL
+
+#endif //CGAL_Triangulation_on_sphere_face_base_2_H
diff --git a/Triangulation_on_sphere_2/include/CGAL/Triangulation_on_sphere_vertex_base_2.h b/Triangulation_on_sphere_2/include/CGAL/Triangulation_on_sphere_vertex_base_2.h
new file mode 100644
index 00000000000..307847c0263
--- /dev/null
+++ b/Triangulation_on_sphere_2/include/CGAL/Triangulation_on_sphere_vertex_base_2.h
@@ -0,0 +1,82 @@
+// Copyright (c) 1997  INRIA Sophia-Antipolis (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)     : Mariette Yvinec
+
+#ifndef CGAL_Triangulation_on_sphere_vertex_base_2_H
+#define CGAL_Triangulation_on_sphere_vertex_base_2_H
+
+#include <CGAL/license/Triangulation_2.h>
+
+#include <CGAL/config.h>
+#include <CGAL/Triangulation_ds_vertex_base_2.h>
+
+namespace CGAL {
+
+template < typename GT,
+           typename Vb = Triangulation_ds_vertex_base_2<> >
+class Triangulation_on_sphere_vertex_base_2
+  : public Vb
+{
+  typedef typename Vb::Triangulation_data_structure                  Tds;
+public:
+  typedef GT                                                         Geom_traits;
+  typedef typename GT::Point_on_sphere                               Point;
+  typedef Tds                                                        Triangulation_data_structure;
+  typedef typename Tds::Face_handle                                  Face_handle;
+  typedef typename Tds::Vertex_handle                                Vertex_handle;
+
+  template < typename TDS2 >
+  struct Rebind_TDS {
+    typedef typename Vb::template Rebind_TDS<TDS2>::Other            Vb2;
+    typedef Triangulation_on_sphere_vertex_base_2<GT, Vb2>           Other;
+  };
+
+private:
+  Point _p;
+
+public:
+  Triangulation_on_sphere_vertex_base_2 () : Vb(), _p() { }
+  Triangulation_on_sphere_vertex_base_2(const Point & p) : Vb(), _p(p) { }
+  Triangulation_on_sphere_vertex_base_2(const Point & p, Face_handle f) : Vb(f), _p(p) { }
+  Triangulation_on_sphere_vertex_base_2(Face_handle f) : Vb(f) { }
+
+  void set_point(const Point & p) { _p = p; }
+  const Point&  point() const { return _p; }
+
+  // the non-const version of point() is undocument but needed to make the point iterator works
+  // using Lutz projection scheme
+  Point& point() { return _p; }
+
+  //the following trivial is_valid to allow
+  // the user of derived face base classes
+  // to add their own purpose checking
+  bool is_valid(bool /* verbose */ = false, int /* level */ = 0) const {return true;}
+};
+
+template < class GT, class Vb >
+std::istream&
+operator>>(std::istream &is, Triangulation_on_sphere_vertex_base_2<GT, Vb> &v)
+  // non combinatorial information. Default = point
+{
+  return is >> static_cast<Vb&>(v) >> v.point();
+}
+
+template < class GT, class Vb >
+std::ostream&
+operator<<(std::ostream &os, const Triangulation_on_sphere_vertex_base_2<GT, Vb> &v)
+  // non combinatorial information. Default = point
+{
+  return os << static_cast<const Vb&>(v) << v.point();
+}
+
+} //namespace CGAL
+
+#endif //CGAL_Triangulation_on_sphere_vertex_base_2_H