diff --git a/Arrangement_on_surface_2/include/CGAL/Arr_spherical_gaussian_map_3/Arr_polyhedral_sgm.h b/Arrangement_on_surface_2/include/CGAL/Arr_spherical_gaussian_map_3/Arr_polyhedral_sgm.h
index ee7de211a40..ca0b1faec2a 100644
--- a/Arrangement_on_surface_2/include/CGAL/Arr_spherical_gaussian_map_3/Arr_polyhedral_sgm.h
+++ b/Arrangement_on_surface_2/include/CGAL/Arr_spherical_gaussian_map_3/Arr_polyhedral_sgm.h
@@ -197,9 +197,6 @@ private:
     /*! The number of facest */
     size_type m_num_facets;
 
-    /*! The type of the facets. */
-    size_type m_num_vertices_per_facet;
-
     /*! The index of the marked vertex */
     size_type m_marked_vertex_index;
 
@@ -216,13 +213,11 @@ private:
                   size_type num_points,
                   const CoordIndexIter& indices_begin,
                   const CoordIndexIter& indices_end,
-                  size_type num_facets,
-                  size_type num_vertices_per_facet = 0) :
+                  size_type num_facets) :
       m_points_begin(points_begin), m_points_end(points_end),
       m_num_points(num_points),
       m_indices_begin(indices_begin), m_indices_end(indices_end),
       m_num_facets(num_facets),
-      m_num_vertices_per_facet(num_vertices_per_facet),
       m_marked_vertex_index(0),
       m_marked_edge_index(0),
       m_marked_facet_index(0)
@@ -257,51 +252,12 @@ private:
 
       // Add the facets:
       counter = 0;
-      switch (m_num_vertices_per_facet) {
-       case 0:          // '0' indicates variant number of vertices per facet
-        {
-         CoordIndexIter ii = m_indices_begin;
-         while (ii != m_indices_end) {
-           Polyhedron_facet_handle fh = B.begin_facet();
-           if (counter == m_marked_facet_index) fh->set_marked(true);
-           int index = *ii++;
-           while (index != -1) {
-             B.add_vertex_to_facet(index);
-             index = *ii++;
-           }
-           B.end_facet();
-           ++counter;
-         }
-        }
-        break;
-
-       case 3:
-        // Unfold for to improve preformance:
-        for (CoordIndexIter ii = m_indices_begin; ii != m_indices_end;
-             ii += m_num_vertices_per_facet)
-        {
-          Polyhedron_facet_handle fh = B.begin_facet();
-          if (counter == m_marked_facet_index) fh->set_marked(true);
-          B.add_vertex_to_facet(*ii);
-          B.add_vertex_to_facet(*(ii+1));
-          B.add_vertex_to_facet(*(ii+2));
-          B.end_facet();
-          ++counter;
-        }
-        break;
-
-       default:
-        for (CoordIndexIter ii = m_indices_begin; ii != m_indices_end;
-             ii += m_num_vertices_per_facet)
-        {
-          Polyhedron_facet_handle fh = B.begin_facet();
-          if (counter == m_marked_facet_index) fh->set_marked(true);
-          for (size_type i = 0; i < m_num_vertices_per_facet; ++i)
-            B.add_vertex_to_facet(*(ii + i));
-          B.end_facet();
-          ++counter;
-        }
-        break;
+      for (auto it = m_indices_begin; it != m_indices_end; ++it) {
+        Polyhedron_facet_handle fh = B.begin_facet();
+        if (counter == m_marked_facet_index) fh->set_marked(true);
+        for (auto index: *it) B.add_vertex_to_facet(index);
+        B.end_facet();
+        ++counter;
       }
       B.end_surface();
     }
@@ -360,13 +316,12 @@ private:
                          size_type num_points,
                          const CoordIndexIter indices_begin,
                          const CoordIndexIter indices_end,
-                         size_type num_facets,
-                         size_type num_vertices_per_facet = 0)
+                         size_type num_facets)
   {
     /*! The builder */
     Build_surface<PointIterator, CoordIndexIter>
       surface(points_begin, points_end, num_points,
-              indices_begin, indices_end, num_facets, num_vertices_per_facet);
+              indices_begin, indices_end, num_facets);
     surface.set_marked_vertex_index(m_marked_vertex_index);
     surface.set_marked_edge_index(m_marked_edge_index);
     surface.set_marked_facet_index(m_marked_facet_index);
@@ -598,15 +553,13 @@ public:
                   const CoordIndexIter indices_begin,
                   const CoordIndexIter indices_end,
                   size_type num_facets,
-                  size_type num_vertices_per_facet = 0,
                   Visitor* visitor = NULL)
   {
     m_visitor = visitor;
 
     Polyhedron polyhedron;
     update_polyhedron(polyhedron, points_begin, points_end, num_points,
-                      indices_begin, indices_end, num_facets,
-                      num_vertices_per_facet);
+                      indices_begin, indices_end, num_facets);
 
 #if 0
     std::copy(polyhedron.points_begin(), polyhedron.points_end(),