diff --git a/Combinatorial_map/include/CGAL/Combinatorial_map.h b/Combinatorial_map/include/CGAL/Combinatorial_map.h
index 5f9f3d96db0..2c95e5219d0 100644
--- a/Combinatorial_map/include/CGAL/Combinatorial_map.h
+++ b/Combinatorial_map/include/CGAL/Combinatorial_map.h
@@ -4360,8 +4360,8 @@ namespace CGAL {
      * @return a dart of the new edge, not incident to the vertex of adart1.
      */
     Dart_handle insert_dangling_cell_1_in_cell_2( Dart_handle adart1,
-                                                  typename Attribute_handle<0>::type
-                                                  ah=null_handle,
+                                                  typename Attribute_handle<0>::
+                                                  type ah=null_handle,
                                                   bool update_attributes=true )
     {
       size_type mark1 = get_new_mark();
@@ -4381,7 +4381,8 @@ namespace CGAL {
 
       size_type treated=get_new_mark();
 
-      CMap_dart_iterator_basic_of_involution<Self,1> it1(*this, adart1, treated);
+      CMap_dart_iterator_basic_of_involution<Self,1>
+          it1(*this, adart1, treated);
 
       for ( ; it1.cont(); ++it1)
       {
@@ -4423,7 +4424,8 @@ namespace CGAL {
               (beta(it1, dim, CGAL_BETAINV(s1), 2), d2, dim);
           }
         }
-        if (are_attributes_automatically_managed() && update_attributes && ah!=NULL)
+        if (are_attributes_automatically_managed() &&
+            update_attributes && ah!=NULL)
         {
           internal::Set_i_attribute_of_dart_functor<Self, 0>::run(this, d1, ah);
         }
diff --git a/Combinatorial_map/include/CGAL/Combinatorial_map_dart.h b/Combinatorial_map/include/CGAL/Combinatorial_map_dart.h
index 33b377357a3..f381e76d773 100644
--- a/Combinatorial_map/include/CGAL/Combinatorial_map_dart.h
+++ b/Combinatorial_map/include/CGAL/Combinatorial_map_dart.h
@@ -239,6 +239,11 @@ namespace CGAL {
     typename Helper::Attribute_handles mattribute_handles;
   };
 
+  /// Old name, kept for backward compatibility
+  template <unsigned int d, typename Refs>
+  struct CGAL_DEPRECATED Dart : public Combinatorial_map_dart<d, Refs>
+  {};
+
 } // namespace CGAL
 
 #endif // CGAL_COMBINATORIAL_MAP_DART_H //
diff --git a/Combinatorial_map/test/Combinatorial_map/Combinatorial_map_3_test.h b/Combinatorial_map/test/Combinatorial_map/Combinatorial_map_3_test.h
index 2cc3a456ec1..466b5fff591 100644
--- a/Combinatorial_map/test/Combinatorial_map/Combinatorial_map_3_test.h
+++ b/Combinatorial_map/test/Combinatorial_map/Combinatorial_map_3_test.h
@@ -1128,8 +1128,6 @@ bool test3D()
   d2 = map.make_combinatorial_hexahedron();
   map.template sew<3>(d1,d2);
   d3 = map.beta(d1, 2);
-  d4 = map.beta(d1, 1,3,1,2);
-  assert(d4==map.beta(d1,1,3,1,2));
   map.display_characteristics(cout) << ", valid=" << map.is_valid() << endl;
   cout << "remove facet4: " << flush; map.template remove_cell<2>(d1);
   map.display_characteristics(cout) << ", valid=" << map.is_valid() << endl;
@@ -1137,6 +1135,18 @@ bool test3D()
   v.push_back(map.beta(v[1],1,2,1)); v.push_back(map.beta(v[2],1,2,1));
   cout << "insert facet4: " << flush; map.insert_cell_2_in_cell_3(v.begin(),v.end());
   map.display_characteristics(cout) << ", valid=" << map.is_valid() << endl;
+
+  Map map2;
+  d1 = map2.make_combinatorial_hexahedron();
+  d2 = map2.make_combinatorial_hexahedron();
+  map2.template sew<3>(d1,d2);
+  if ( !map.is_isomorphic_to(map2) )
+  {
+    std::cout<<"Error: map and map2 are not isomorphic (after insertion/removal).\n";
+    assert(false);
+    return false;
+  }
+
   map.clear(); v.clear();
 
   cout << "***************************** TEST INSERT FACET 3D DONE."