diff --git a/AABB_tree/doc/AABB_tree/PackageDescription.txt b/AABB_tree/doc/AABB_tree/PackageDescription.txt
index eebd2bd7a0b..c70c2ab611a 100644
--- a/AABB_tree/doc/AABB_tree/PackageDescription.txt
+++ b/AABB_tree/doc/AABB_tree/PackageDescription.txt
@@ -36,6 +36,6 @@
 - `CGAL::AABB_triangle_primitive<GeomTraits, Iterator, CacheDatum>`
 - `CGAL::AABB_segment_primitive<GeomTraits, Iterator, CacheDatum>`
 - `CGAL::AABB_primitive<Id,ObjectPropertyMap,PointPropertyMapPolyhedron,ExternalPropertyMaps,CacheDatum>`
-- `CGAL::AABB_halfedge_graph_segment_primitive<HalfedgeGraph,OneHalfedgeGraphPerTree,CacheDatum>`
-- `CGAL::AABB_face_graph_triangle_primitive<FaceGraph,OneFaceGraphPerTree,CacheDatum>`
+- `CGAL::AABB_halfedge_graph_segment_primitive<HalfedgeGraph,Vpm,OneHalfedgeGraphPerTree,CacheDatum>`
+- `CGAL::AABB_face_graph_triangle_primitive<FaceGraph,Vpm,OneFaceGraphPerTree,CacheDatum>`
 */
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_slicer.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_slicer.h
index b9cba19d237..b3dc43477a5 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_slicer.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_slicer.h
@@ -39,6 +39,8 @@
 #include <CGAL/Polygon_mesh_processing/internal/Polygon_mesh_slicer/Axis_parallel_plane_traits.h>
 
 #include <boost/variant.hpp>
+#include <boost/mpl/if.hpp>
+#include <boost/type_traits/is_same.hpp>
 
 #include <CGAL/boost/graph/split_graph_into_polylines.h>
 #include <CGAL/boost/graph/helpers.h>
@@ -86,7 +88,13 @@ template<class TriangleMesh,
   class VertexPointMap = typename boost::property_map< TriangleMesh, vertex_point_t>::type,
   class AABBTree = AABB_tree<
                        AABB_traits<Traits,
-                         AABB_halfedge_graph_segment_primitive<TriangleMesh> > >,
+                         AABB_halfedge_graph_segment_primitive<TriangleMesh,
+                                                                typename boost::mpl::if_<
+                                                                  typename boost::is_same<
+                                                                    VertexPointMap,
+                                                                    typename boost::property_map< TriangleMesh, vertex_point_t>::type >::type,
+                                                                  Default,
+                                                                  VertexPointMap>::type> > >,
   bool UseParallelPlaneOptimization=true>
 class Polygon_mesh_slicer
 {
@@ -393,6 +401,9 @@ class Polygon_mesh_slicer
 
 public:
 
+  /// the AABB-tree type used internally
+  typedef AABBTree AABB_tree;
+
   /**
   * Constructor using `edges(tmesh)` to initialize the
   * internal `AABB_tree`.