diff --git a/BGL/include/CGAL/boost/graph/generators.h b/BGL/include/CGAL/boost/graph/generators.h
index a4e91f177fb..842cc1dfdfe 100644
--- a/BGL/include/CGAL/boost/graph/generators.h
+++ b/BGL/include/CGAL/boost/graph/generators.h
@@ -348,6 +348,22 @@ make_hexahedron(const P& p0, const P& p1, const P& p2, const P& p3,
   return next(next(hb, g), g);
 }
 
+/**
+ * \ingroup PkgBGLHelperFct
+ * \tparam IsoCuboid model of `IsoCuboid_3`
+ * \brief creates an isolated hexahedron
+ * equivalent to `c`, and adds it to the graph `g`.
+ * \returns the halfedge that has the target vertex associated with `c.min()`,
+ * in the bottom face of the cuboid.
+ **/
+template<typename Graph, typename IsoCuboid>
+typename boost::graph_traits<Graph>::halfedge_descriptor
+make_hexahedron(const IsoCuboid& c, Graph& g)
+{
+  return CGAL::make_hexahedron(c[0], c[1], c[2], c[3],
+                               c[4], c[5], c[6], c[7], g);
+}
+
 /**
  * \ingroup PkgBGLHelperFct
  * \brief creates an isolated tetrahedron
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h
index 5660a7cfdd5..015265a48bd 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h
@@ -331,18 +331,13 @@ namespace CGAL {
 
       using GT = typename GetGeomTraits<PolygonMesh, NamedParameters>::type;
       GT gt = choose_parameter<GT>(get_parameter(np, internal_np::geom_traits));
-      using Point_3 = typename GT::Point_3;
       using Iso_cuboid_3 = typename GT::Iso_cuboid_3;
-      using Vector_3 = typename GT::Vector_3;
 
       const bool dont_triangulate = choose_parameter(
         get_parameter(np, internal_np::do_not_triangulate_faces), false);
 
-      const Iso_cuboid_3 bbext(CGAL::Polygon_mesh_processing::bbox(pmesh, np));
-
       PolygonMesh bbox_mesh;
-      CGAL::make_hexahedron(bbext[0], bbext[1], bbext[2], bbext[3],
-                            bbext[4], bbext[5], bbext[6], bbext[7],
+      CGAL::make_hexahedron(Iso_cuboid_3(bbox(pmesh, np)),
                             bbox_mesh);
 
       if(!dont_triangulate)