diff --git a/Triangulation/benchmark/Triangulation/bench6d.cpp b/Triangulation/benchmark/Triangulation/bench6d.cpp
index a14dba4bed4..90fc41c680a 100644
--- a/Triangulation/benchmark/Triangulation/bench6d.cpp
+++ b/Triangulation/benchmark/Triangulation/bench6d.cpp
@@ -50,6 +50,7 @@ int main(int argc, char* argv[])
     std::vector<Triangulation::Full_cell_handle> infinite_cells;
     t.tds().incident_full_cells(t.infinite_vertex(), std::back_inserter(infinite_cells));
 
+    return 0;
     std::set<std::pair<std::ptrdiff_t, std::ptrdiff_t>> edges;
 
     for(auto ch : infinite_cells) {
diff --git a/Triangulation/doc/Triangulation/CGAL/Triangulation.h b/Triangulation/doc/Triangulation/CGAL/Triangulation.h
index 32188c44323..49ffb246f1c 100644
--- a/Triangulation/doc/Triangulation/CGAL/Triangulation.h
+++ b/Triangulation/doc/Triangulation/CGAL/Triangulation.h
@@ -520,7 +520,7 @@ position `p`. Returns a handle to that vertex.
 \pre The boundary of the union of full cells incident to `f` must be a triangulation of a
 sphere of dimension `tr`.`current_dimension()`).
 */
-Vertex_handle collapse_face(const Point & p, const Face & f);
+Vertex_handle contract_face(const Point & p, const Face & f);
 
 /// @}
 
diff --git a/Triangulation/doc/Triangulation/Concepts/TriangulationDataStructure.h b/Triangulation/doc/Triangulation/Concepts/TriangulationDataStructure.h
index e9d3d22a209..370bbad3e8e 100644
--- a/Triangulation/doc/Triangulation/Concepts/TriangulationDataStructure.h
+++ b/Triangulation/doc/Triangulation/Concepts/TriangulationDataStructure.h
@@ -456,14 +456,14 @@ Insertion in a hole, \f$ d=2\f$
 \cgalAdvancedEnd
 */
 template< class ForwardIterator > Vertex_handle
-insert_in_hole(ForwardIterator start, ForwardIterator end, Facet f);
+insert_in_hole(ForwardIterator s, ForwardIterator e, Facet f);
 
 /*!
 Same as above, but handles to the new full cells are
 appended to the `out` output iterator.
 */
 template< class ForwardIterator, class OutputIterator >
-Vertex_handle insert_in_hole(ForwardIterator start, ForwardIterator end, Facet
+Vertex_handle insert_in_hole(ForwardIterator s, ForwardIterator e, Facet
 f, OutputIterator out);
 
 /*!
@@ -594,7 +594,7 @@ Calls `delete_full_cell` over an iterator range of value type `Full_cell_handle`
 \cgalAdvancedEnd
 */
 template< typename ForwardIterator > void
-delete_full_cells(ForwardIterator start, ForwardIterator end);
+delete_full_cells(ForwardIterator s, ForwardIterator e);
 
 /// @}
 
diff --git a/Triangulation/include/CGAL/Triangulation_data_structure.h b/Triangulation/include/CGAL/Triangulation_data_structure.h
index 37fbd8914e9..10e71e9178e 100644
--- a/Triangulation/include/CGAL/Triangulation_data_structure.h
+++ b/Triangulation/include/CGAL/Triangulation_data_structure.h
@@ -309,10 +309,10 @@ public:
         return s->mirror_index(i);
     }
 
-    int mirror_vertex(Full_cell_handle s, int i) const /* Concept */
+    Vertex_handle mirror_vertex(Full_cell_handle s, int i) const /* Concept */
     {
         CGAL_precondition(Full_cell_handle() != s && check_range(i));
-        return s->mirror_vertex(i);
+        return s->mirror_vertex(i, current_dimension);
     }
 
     // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - FACETS OPERATIONS