diff --git a/Operations_on_polyhedra/include/CGAL/internal/corefinement/Combinatorial_map_output_builder.h b/Operations_on_polyhedra/include/CGAL/internal/corefinement/Combinatorial_map_output_builder.h
index 16c823a715d..a86ab3d1098 100644
--- a/Operations_on_polyhedra/include/CGAL/internal/corefinement/Combinatorial_map_output_builder.h
+++ b/Operations_on_polyhedra/include/CGAL/internal/corefinement/Combinatorial_map_output_builder.h
@@ -48,7 +48,7 @@ next_marked_dart_around_target_vertex(
   CGAL_precondition(final_map.is_marked(dart,mark_index));
   typename Combinatorial_map_3::Dart_handle next=dart->beta(1);
   while ( ! final_map.is_marked(next,mark_index) ) {
-    if (next->is_free(2) )//we reach a boundary
+    if (final_map.is_free(next,2) )//we reach a boundary
       return  boost::optional<typename Combinatorial_map_3::Dart_handle>();
     next=next->beta(2)->beta(1);
   }
@@ -71,7 +71,7 @@ get_next_marked_dart_around_target_vertex(
   CGAL_precondition(final_map.is_marked(dart,mark_index));
   typename Combinatorial_map_3::Dart_handle next=dart->beta(1);
   while ( !final_map.is_marked(next,mark_index) ) {
-    CGAL_assertion( !next->is_free(2) );
+    CGAL_assertion( !final_map.is_free(next,2) );
     next=next->beta(2)->beta(1);
     CGAL_assertion(next != dart);
   }
@@ -92,7 +92,7 @@ get_next_marked_dart_around_source_vertex(
   CGAL_precondition(final_map.is_marked(dart,mark_index));
   typename Combinatorial_map_3::Dart_handle next=dart->beta(0);
   while ( ! final_map.is_marked(next,mark_index) ) {
-    CGAL_assertion( !next->is_free(2) );
+    CGAL_assertion( !final_map.is_free(next,2) );
     next=next->beta(2)->beta(0);
     CGAL_assertion(next != dart);
   }
@@ -114,8 +114,8 @@ void sew_2_marked_darts( Combinatorial_map_3& final_map,
                          const std::pair<int,int>& indices,
                          const std::pair<bool,int>& polyline_info)
 {
-  CGAL_precondition( dart_1->is_free(2) );
-  CGAL_precondition( dart_2->is_free(2) );
+  CGAL_precondition( final_map.is_free(dart_1, 2) );
+  CGAL_precondition( final_map.is_free(dart_2, 2) );
   CGAL_precondition( final_map.is_marked(dart_1,mark_index) );
   CGAL_precondition( final_map.is_marked(dart_2,mark_index) );
   CGAL_precondition( dart_1->template attribute<0>()->point() ==
@@ -200,7 +200,7 @@ void sew_3_marked_darts( Combinatorial_map_3& final_map,
   //set to be removed the darts of the two no longer used volumes
   typename Combinatorial_map_3::Dart_handle start=not_top;
   do {
-    CGAL_assertion(!not_top->is_free(3));
+    CGAL_assertion(!final_map.is_free(not_top, 3));
     darts_to_remove.insert(not_top);
     darts_to_remove.insert(not_top->beta(1));
     darts_to_remove.insert(not_top->beta(1)->beta(1));