diff --git a/Combinatorial_map/examples/Combinatorial_map/map_3_constructor.cpp b/Combinatorial_map/examples/Combinatorial_map/map_3_constructor.cpp
new file mode 100644
index 00000000000..d34e7b24265
--- /dev/null
+++ b/Combinatorial_map/examples/Combinatorial_map/map_3_constructor.cpp
@@ -0,0 +1,24 @@
+#include <CGAL/Combinatorial_map.h>
+#include <CGAL/Combinatorial_map_incremental_builder.h>
+#include <iostream>
+#include <cstdlib>
+
+typedef CGAL::Combinatorial_map<2> CMap;
+
+int main()
+{
+  CMap cm;
+  CGAL::Combinatorial_map_incremental_builder<CMap> b(cm);
+
+  b.begin_surface(0,0,0);
+  b.add_facet("a b c -a -b");
+  b.add_facet("-c d e -d -e");
+  b.end_surface();
+  
+  // Display the combinatorial map characteristics.
+  cm.display_characteristics(std::cout);
+  std::cout<<", valid="<<cm.is_valid()<<std::endl;
+
+  return EXIT_SUCCESS;
+}
+
diff --git a/Combinatorial_map/include/CGAL/Combinatorial_map_incremental_builder.h b/Combinatorial_map/include/CGAL/Combinatorial_map_incremental_builder.h
new file mode 100644
index 00000000000..aad1af7e6bc
--- /dev/null
+++ b/Combinatorial_map/include/CGAL/Combinatorial_map_incremental_builder.h
@@ -0,0 +1,286 @@
+// Copyright (c) 2011 CNRS and LIRIS' Establishments (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 Lesser General Public License as
+// published by the Free Software Foundation; either version 3 of the License,
+// 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: LGPL-3.0+
+//
+// Author(s)     : Guillaume Damiand <guillaume.damiand@liris.cnrs.fr>
+//
+#ifndef CGAL_COMBINATORIAL_MAP_INCREMENTAL_BUILDER_H
+#define CGAL_COMBINATORIAL_MAP_INCREMENTAL_BUILDER_H 1
+
+#include <vector>
+#include <unordered_map>
+#include <cstddef>
+
+namespace CGAL {
+  struct Combinatorial_map_tag;
+  struct Generalized_map_tag;
+  
+  template<class CMAP, class Combinatorial_data_structure=
+           typename CMAP::Combinatorial_data_structure>
+  struct Add_vertex_to_face
+  {
+    static typename CMAP::Dart_handle run(CMAP&,
+                                         typename CMAP::Dart_handle)
+    {}
+  };
+  template<class CMAP>
+  struct Add_vertex_to_face<CMAP, Combinatorial_map_tag>
+  {
+    static typename CMAP::Dart_handle run(CMAP& cmap,
+                                         typename CMAP::Dart_handle prev_dart)
+    {
+      typename CMAP::Dart_handle res=cmap.create_dart();
+      if (prev_dart!=cmap.null_handle)
+      {
+        cmap.template link_beta<1>(prev_dart, res);
+      }
+      return res;
+    }
+    static void run_for_last(CMAP&,
+                             typename CMAP::Dart_handle)
+    { // here nothing to do, all darts were already created.
+    }
+  };
+  template<class CMAP>
+  struct Add_vertex_to_face<CMAP, Generalized_map_tag>
+  {
+    static typename CMAP::Dart_handle run(CMAP& cmap,
+                                         typename CMAP::Dart_handle prev_dart)
+    {
+      typename CMAP::Dart_handle res=cmap.create_dart();
+      if (prev_dart!=cmap.null_handle)
+      {
+        cmap.template link_alpha<0>(prev_dart, res);
+        cmap.template link_alpha<1>(res, cmap.create_dart());
+        res=cmap.template alpha<1>(res);
+      }
+      return res;
+    }
+    static void run_for_last(CMAP& cmap,
+                             typename CMAP::Dart_handle prev_dart)
+    {
+      // here we need to create a last dart and 0-link it
+      assert(prev_dart!=cmap.null_handle);
+      cmap.template link_alpha<0>(prev_dart, cmap.create_dart());
+    }
+  };
+
+  // Incremental builder
+  template < class CMap_ >
+  class Combinatorial_map_incremental_builder
+  {
+  public:
+    typedef CMap_                      CMap;
+    typedef typename CMap::Dart_handle Dart_handle;
+    typedef typename CMap::size_type   size_type;
+
+    Combinatorial_map_incremental_builder(CMap & acmap) :
+      cmap(acmap),
+      first_dart(cmap.null_handle),
+      prev_dart(cmap.null_handle),
+      used_add_vertex(false),
+      used_add_edge(false)
+    {}
+
+    void begin_facet()
+    {
+      first_dart = cmap.null_handle;
+      prev_dart  = cmap.null_handle;
+      // std::cout<<"Begin facet: "<<std::flush;
+    }
+
+    void add_vertex_to_facet(size_type i)
+    {
+      if (used_add_edge)
+      {
+        std::cerr<<"Combinatorial_map_incremental_builder ERROR: you cannot mix add_edge_to_facet"
+                 <<" and add_vertex_to_facet for a same builder."<<std::endl;
+        return;
+      }
+      used_add_vertex=true;
+        
+      CGAL_assertion( i<new_vertices );
+      // std::cout<<i<<"  "<<std::flush;
+      Dart_handle cur = Add_vertex_to_face<CMap>::run(cmap, prev_dart);
+
+      if ( prev_dart!=cmap.null_handle )
+      {
+        Dart_handle opposite=find_dart_between(i, prev_vertex);
+        if ( opposite!=cmap.null_handle )
+        {
+          CGAL_assertion( cmap.template is_free<2>(opposite) );
+          cmap.template set_opposite<2>(prev_dart, opposite);
+        }
+
+        add_dart_in_vertex_to_dart_map(prev_dart, prev_vertex, i);
+      }
+      else
+      {
+        first_dart   = cur;
+        first_vertex = i;
+      }
+
+      prev_dart   = cur;
+      prev_vertex = i;
+    }
+
+    // Add one edge to the current facet, given by its label (any string, using minus sign for orientation) 
+    void add_edge_to_facet(const std::string& s)
+    {
+      if (used_add_vertex)
+      {
+        std::cerr<<"Combinatorial_map_incremental_builder ERROR: you cannot mix add_edge_to_facet"
+                 <<" and add_vertex_to_facet for a same builder."<<std::endl;
+        return;
+      }
+      used_add_edge=true;
+
+      assert(edge_label_to_dart.count(s)==0); // Since we have an orientable surface,
+                                              // we cannot use a same edge twice.
+
+      Dart_handle cur = Add_vertex_to_face<CMap>::run(cmap, prev_dart);
+      auto ite=edge_label_to_dart.find(opposite_label(s));
+
+      if (ite!=edge_label_to_dart.end())
+      {
+        CGAL_assertion( cmap.template is_free<2>(ite->second) );
+        cmap.template set_opposite<2>(cur, ite->second);
+      }
+
+      edge_label_to_dart[s]=cur;
+
+      if (prev_dart==cmap.null_handle)
+      { first_dart=cur; }
+
+      prev_dart=cur;
+    }
+
+    // add one facet, s is a sequence of labels, add all the corresponding edges into the current facet.
+    void add_facet(const std::string& s)
+    {
+      begin_facet();
+      
+      std::istringstream iss(s);
+      for (std::string token; std::getline(iss, token, ' '); )
+      { add_edge_to_facet(token); }
+
+      end_facet();
+    }
+
+    // End of the facet. Return the first dart of this facet.
+    Dart_handle end_facet()
+    {
+      CGAL_assertion( first_dart!=cmap.null_handle && prev_dart!=cmap.null_handle );
+
+      if (used_add_vertex)
+      {
+        Add_vertex_to_face<CMap>::run_for_last(cmap, prev_dart);
+        cmap.set_next(prev_dart, first_dart);
+
+        Dart_handle opposite=find_dart_between(first_vertex, prev_vertex);
+        if ( opposite!=cmap.null_handle )
+        {
+          CGAL_assertion( cmap.template is_free<2>(opposite) );
+          cmap.template set_opposite<2>(prev_dart, opposite);
+        }
+
+        add_dart_in_vertex_to_dart_map(prev_dart, prev_vertex, first_vertex);
+      }
+      else
+      {
+        cmap.set_next(prev_dart, first_dart);
+      }
+      
+      return first_dart;
+    }
+
+    void begin_surface( std::size_t v, std::size_t /*f*/, std::size_t h)
+    {
+      new_vertices  = 0;
+      first_dart    = cmap.null_handle;
+      prev_dart     = cmap.null_handle;
+
+      vertex_to_dart_map.clear();
+      vertex_to_dart_map.reserve(v);
+
+      edge_label_to_dart.clear();
+      edge_label_to_dart.reserve(h/2);
+      
+      used_add_vertex=false;
+      used_add_edge=false;
+      
+      // cmap.reserve(v,h);
+    }
+
+    // End of the surface. Return one dart of the created surface.
+    Dart_handle end_surface()
+    { return first_dart; }
+
+  protected:
+
+    Dart_handle find_dart_between(size_type i, size_type j)
+    {
+      typename std::vector<std::pair<Dart_handle, size_type> >::reverse_iterator
+        it(vertex_to_dart_map[i].rbegin());
+      typename std::vector<std::pair<Dart_handle, size_type> >::reverse_iterator
+        itend(vertex_to_dart_map[i].rend());
+
+      for ( ; it!=itend; ++it )
+      {
+        if ( it->second==j ) return (it->first);
+      }
+      return cmap.null_handle;
+    }
+
+    void add_dart_in_vertex_to_dart_map(Dart_handle adart, size_type i, size_type j)
+    {
+      CGAL_assertion( adart!=cmap.null_handle );
+      vertex_to_dart_map[i].push_back(std::make_pair(adart, j));
+    }
+
+    std::string opposite_label(const std::string & s)
+    {
+      assert(!s.empty());
+      if (s[0]=='-')
+      { return s.substr(1, std::string::npos); }
+
+      return std::string("-")+s;
+    }
+    
+  private:
+    // For vertex number i, vector of all vertices linked to i with an edge (dart of the edge and index
+    // of the second vertex). TODO use a std::unordered_map instead of the second vector
+    typedef std::vector<std::vector<std::pair<Dart_handle, size_type> > > Vertex_to_dart_array;
+    Vertex_to_dart_array vertex_to_dart_map;
+
+    // For edge label, its corresponding dart. For an edge a -a, stores its two darts in two different entries.
+    std::unordered_map<std::string, Dart_handle> edge_label_to_dart;
+    
+    CMap&       cmap;
+    Dart_handle first_dart;
+    Dart_handle prev_dart;
+    size_type   first_vertex;
+    size_type   prev_vertex;
+    size_type   new_vertices;
+    bool        used_add_vertex;
+    bool        used_add_edge;
+  };
+
+} //namespace CGAL
+
+#endif // CGAL_COMBINATORIAL_MAP_INCREMENTAL_BUILDER_H //
+// EOF //