diff --git a/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/create_offset_polygons_from_polygon_with_holes_2.h b/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/create_offset_polygons_from_polygon_with_holes_2.h
index 5c2d651e14f..b9a5ca632cc 100644
--- a/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/create_offset_polygons_from_polygon_with_holes_2.h
+++ b/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/create_offset_polygons_from_polygon_with_holes_2.h
@@ -8,11 +8,11 @@ holes</I> at distance `offset` of the 2D polygon `poly`.
 
 This is equivalent to `arrange_offset_polygons_2(create_exterior_skeleton_and_offset_polygons_2(offset,poly,okk,ssk))`.
 */
-template<class FT, class OffsettingK, class SkeletonK>
-std::vector< boost::shared_ptr< Polygon_with_holes_2<OffsettingK> > >
+template<class FT, class OffsettingK, class SkeletonK, class C>
+std::vector< boost::shared_ptr< Polygon_with_holes_2<OffsettingK,C> > >
 create_exterior_skeleton_and_offset_polygons_with_holes_2 
   ( FT offset
-  , CGAL::Polygon_2<OffsettingK> poly_with_holes
+  , CGAL::Polygon_2<OffsettingK,C> poly_with_holes
   , OffsettingK ofk = Exact_predicates_inexact_constructions_kernel
   , SkeletonK ssk   = Exact_predicates_inexact_constructions_kernel
   ) ;
@@ -32,19 +32,20 @@ A temporary straight skeleton is constructed in the interior of the input polygo
    If `SkeletonK != OffsettingK` the constructed straight skeleton
    is converted to `Straight_skeleton_2<OffsettingK>`.
 3. `FT` is any number type implicitly convertible to `OffsettingK::FT`.
-3. `Straight_skeleton` is `Straight_skeleton_2<K2>`. 
+4. `C` is the container of points in the polygons.
+5. `Straight_skeleton` is `Straight_skeleton_2<K2>`. 
    If `K != K2` the straight skeleton is converted to `Straight_skeleton_2<K>`.
-4. `HoleIterator::value_type` and `Polygon` are `Polygon_2<OffsettingK>`
+6. `HoleIterator::value_type` and `Polygon` are `Polygon_2<OffsettingK>`
    or a standard container of `OffsettingK::Point_2` elements.
 
 \sa `create_exterior_straight_skeleton_2`
 \sa `Straight_skeleton_builder_2<Gt,Ss>` 
 
 */
-template<class FT, class OffsettingK, class SkeletonK>
-std::vector< boost::shared_ptr< Polygon_2<OffsettingK> > >
+template<class FT, class OffsettingK, class SkeletonK, class C>
+std::vector< boost::shared_ptr< Polygon_2<OffsettingK,C> > >
 create_interior_skeleton_and_offset_polygons_2 ( FT offset
-                                               , CGAL::Polygon_with_holes<OffsettingK> poly_with_holes
+                                               , CGAL::Polygon_with_holes<OffsettingK,C> poly_with_holes
                                                , OffsettingK ofk 
                                                   = CGAL::Exact_predicates_inexact_constructions_kernel
                                                , SkeletonK ssk 
@@ -66,20 +67,21 @@ This is equivalent to `arrange_offset_polygons_2(create_interior_skeleton_and_of
    If `SkeletonK != OffsettingK` the constructed straight skeleton
    is converted to `Straight_skeleton_2<OffsettingK>`.
 3. `FT` is any number type implicitly convertible to `OffsettingK::FT`.
-3. `Straight_skeleton` is `Straight_skeleton_2<K2>`. 
+4. `C` is the container of points in the polygons.
+5. `Straight_skeleton` is `Straight_skeleton_2<K2>`. 
    If `K != K2` the straight skeleton is converted to `Straight_skeleton_2<K>`.
-4. `HoleIterator::value_type` and `Polygon` are `CGAL::Polygon_2<OffsettingK>`
+6. `HoleIterator::value_type` and `Polygon` are `CGAL::Polygon_2<OffsettingK>`
    or a standard container of `OffsettingK::Point_2` elements.
 
 \sa `create_exterior_straight_skeleton_2`
 \sa `Straight_skeleton_builder_2<Gt,Ss>` 
 
 */
-template<class FT, class OffsettingK, class SkeletonK>
-std::vector< boost::shared_ptr< Polygon_with_holes_2<OffsettingK> > >
+template<class FT, class OffsettingK, class SkeletonK, class C>
+std::vector< boost::shared_ptr< Polygon_with_holes_2<OffsettingK,C> > >
 create_interior_skeleton_and_offset_polygons_with_holes_2 
   ( FT offset
-  , CGAL::Polygon_2<OffsettingK> poly
+  , CGAL::Polygon_2<OffsettingK,C> poly
   , OffsettingK ofk = CGAL::Exact_predicates_inexact_constructions_kernel
   , SkeletonK ssk   = CGAL::Exact_predicates_inexact_constructions_kernel
   ) ;
@@ -99,20 +101,21 @@ This is equivalent to `arrange_offset_polygons_2(create_interior_skeleton_and_of
    If `SkeletonK != OffsettingK` the constructed straight skeleton
    is converted to `Straight_skeleton_2<OffsettingK>`.
 3. `FT` is any number type implicitly convertible to `OffsettingK::FT`.
-3. `Straight_skeleton` is `Straight_skeleton_2<K2>`. 
+4. `C` is the container of points in the polygons.
+5. `Straight_skeleton` is `Straight_skeleton_2<K2>`. 
    If `K != K2` the straight skeleton is converted to `Straight_skeleton_2<K>`.
-4. `HoleIterator::value_type` and `Polygon` are `CGAL::Polygon_2<OffsettingK>`
+6. `HoleIterator::value_type` and `Polygon` are `CGAL::Polygon_2<OffsettingK>`
    or a standard container of `OffsettingK::Point_2` elements.
 
 \sa `create_exterior_straight_skeleton_2`
 \sa `Straight_skeleton_builder_2<Gt,Ss>` 
 
 */
-template<class FT, class OffsettingK, class SkeletonK>
-std::vector< boost::shared_ptr< Polygon_with_holes_2<OffsettingK> > >
+template<class FT, class OffsettingK, class SkeletonK, class C>
+std::vector< boost::shared_ptr< Polygon_with_holes_2<OffsettingK,C> > >
 create_interior_skeleton_and_offset_polygons_with_holes_2 
   ( FT offset
-  , CGAL::Polygon_with_holes_2<OffsettingK> poly_with_holes
+  , CGAL::Polygon_with_holes_2<OffsettingK,C> poly_with_holes
   , OffsettingK ofk = CGAL::Exact_predicates_inexact_constructions_kernel
   , SkeletonK ssk   = CGAL::Exact_predicates_inexact_constructions_kernel
   ) ;
diff --git a/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/create_straight_skeleton_from_polygon_with_holes_2.h b/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/create_straight_skeleton_from_polygon_with_holes_2.h
index 5ac7570128b..b74ae3ed8e0 100644
--- a/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/create_straight_skeleton_from_polygon_with_holes_2.h
+++ b/Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/create_straight_skeleton_from_polygon_with_holes_2.h
@@ -9,9 +9,9 @@ returns a new `Straight_skeleton_2<K>` in the interior of the 2D polygon with ho
 \sa `Straight_skeleton_builder_2<Gt,Ss>` 
 
 */
-template<class K>
+  template<class K, class C>
 boost::shared_ptr< Straight_skeleton_2<K> >
-create_interior_straight_skeleton_2 ( Polygon_with_holes<K> poly_with_holes
+  create_interior_straight_skeleton_2 ( Polygon_with_holes<K,C> poly_with_holes
                                     , K const&  k = Exact_predicates_inexact_constructions_kernel
                                     ) ;
 } /* namespace CGAL */
diff --git a/Straight_skeleton_2/include/CGAL/create_offset_polygons_from_polygon_with_holes_2.h b/Straight_skeleton_2/include/CGAL/create_offset_polygons_from_polygon_with_holes_2.h
index b9b9d1e0926..2353f887a0d 100644
--- a/Straight_skeleton_2/include/CGAL/create_offset_polygons_from_polygon_with_holes_2.h
+++ b/Straight_skeleton_2/include/CGAL/create_offset_polygons_from_polygon_with_holes_2.h
@@ -26,7 +26,7 @@
 
 namespace CGAL {
 
-template<class FT, class OfK, class C, class SsK>
+template<class FT, class OfK, class SsK, class C>
 std::vector< boost::shared_ptr< Polygon_2<OfK,C> > >
 inline
 create_interior_skeleton_and_offset_polygons_2 ( FT const& aOffset, Polygon_with_holes_2<OfK,C> const& aPoly, SsK const& ssk )
@@ -65,7 +65,7 @@ create_exterior_skeleton_and_offset_polygons_with_holes_2 ( FT const&
                                   );
 }
 
-template<class OfK, class C, class SsK, class FT>
+  template<class FT, class OfK, class SsK, class C>
 std::vector< boost::shared_ptr< Polygon_with_holes_2<OfK,C> > >
 inline
 create_interior_skeleton_and_offset_polygons_with_holes_2 ( FT const& aOffset, Polygon_with_holes_2<OfK,C> const& aPoly, SsK const& ssk )
@@ -74,7 +74,7 @@ create_interior_skeleton_and_offset_polygons_with_holes_2 ( FT const& aOffset, P
 }
 
 
-template<class OfK, class C, class FT>
+  template<class FT, class OfK, class C>
 std::vector< boost::shared_ptr< Polygon_with_holes_2<OfK,C> > >
 inline
 create_interior_skeleton_and_offset_polygons_with_holes_2 ( FT const& aOffset, Polygon_with_holes_2<OfK,C> const& aPoly )
diff --git a/Straight_skeleton_2/include/CGAL/create_straight_skeleton_from_polygon_with_holes_2.h b/Straight_skeleton_2/include/CGAL/create_straight_skeleton_from_polygon_with_holes_2.h
index 8e64947cdd8..e4fa61c31b9 100644
--- a/Straight_skeleton_2/include/CGAL/create_straight_skeleton_from_polygon_with_holes_2.h
+++ b/Straight_skeleton_2/include/CGAL/create_straight_skeleton_from_polygon_with_holes_2.h
@@ -25,10 +25,10 @@
 
 namespace CGAL {
 
-template<class K>
+template<class K, class C>
 boost::shared_ptr< Straight_skeleton_2<K> >
 inline
-create_interior_straight_skeleton_2 ( Polygon_with_holes_2<K> const& aPolyWithHoles )
+create_interior_straight_skeleton_2 ( Polygon_with_holes_2<K,C> const& aPolyWithHoles )
 {
   return create_interior_straight_skeleton_2(aPolyWithHoles.outer_boundary().vertices_begin()
                                             ,aPolyWithHoles.outer_boundary().vertices_end  ()