diff --git a/Stream_support/include/CGAL/IO/GOCAD.h b/Stream_support/include/CGAL/IO/GOCAD.h
index f0bab7148bb..5fe66515fe0 100644
--- a/Stream_support/include/CGAL/IO/GOCAD.h
+++ b/Stream_support/include/CGAL/IO/GOCAD.h
@@ -332,9 +332,9 @@ bool write_GOCAD(std::ostream& os,
  *
  * \cgalNamedParamsBegin
  *   \cgalParamNBegin{point_map}
- *     \cgalParamDescription{a property map associating points with floating point coordinates to the elements of the point set `points`}
+ *     \cgalParamDescription{a property map associating points with %Cartesian coordinates to the elements of the point set `points`}
  *     \cgalParamType{a model of `ReadablePropertyMap` whose key type is the value type
- *                    of the iterator of `PointRange` and value type is a point type with floating point coordinates}
+ *                    of the iterator of `PointRange` and value type is a point type with %Cartesian coordinates}
  *     \cgalParamDefault{`CGAL::Identity_property_map<std::iterator_traits<PointRange::iterator>::value_type>`}
  *   \cgalParamNEnd
  *   \cgalParamNBegin{stream_precision}
@@ -379,6 +379,12 @@ bool write_GOCAD(std::ostream& os,
  * \param np optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
  *
  * \cgalNamedParamsBegin
+ *   \cgalParamNBegin{point_map}
+ *     \cgalParamDescription{a property map associating points with %Cartesian coordinates to the elements of the point set `points`}
+ *     \cgalParamType{a model of `ReadablePropertyMap` whose key type is the value type
+ *                    of the iterator of `PointRange` and value type is a point type with %Cartesian coordinates}
+ *     \cgalParamDefault{`CGAL::Identity_property_map<std::iterator_traits<PointRange::iterator>::value_type>`}
+ *   \cgalParamNEnd
  *   \cgalParamNBegin{stream_precision}
  *     \cgalParamDescription{a parameter used to set the precision (i.e. how many digits are generated) of the output stream}
  *     \cgalParamType{int}
diff --git a/Stream_support/include/CGAL/IO/OBJ.h b/Stream_support/include/CGAL/IO/OBJ.h
index 924e2353172..74b46a457ae 100644
--- a/Stream_support/include/CGAL/IO/OBJ.h
+++ b/Stream_support/include/CGAL/IO/OBJ.h
@@ -315,9 +315,9 @@ bool read_OBJ(const std::string& fname,
  *
  * \cgalNamedParamsBegin
  *   \cgalParamNBegin{point_map}
- *     \cgalParamDescription{a property map associating points with floating point coordinates to the elements of the point set `points`}
+ *     \cgalParamDescription{a property map associating points with %Cartesian coordinates to the elements of the point set `points`}
  *     \cgalParamType{a model of `ReadablePropertyMap` whose key type is the value type
- *                    of the iterator of `PointRange` and value type is a point type with floating point coordinates}
+ *                    of the iterator of `PointRange` and value type is a point type with %Cartesian coordinates}
  *     \cgalParamDefault{`CGAL::Identity_property_map<std::iterator_traits<PointRange::iterator>::value_type>`}
  *   \cgalParamNEnd
  *   \cgalParamNBegin{stream_precision}
@@ -364,6 +364,12 @@ bool write_OBJ(std::ostream& os,
  * \param np optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
  *
  * \cgalNamedParamsBegin
+ *   \cgalParamNBegin{point_map}
+ *     \cgalParamDescription{a property map associating points with %Cartesian coordinates to the elements of the point set `points`}
+ *     \cgalParamType{a model of `ReadablePropertyMap` whose key type is the value type
+ *                    of the iterator of `PointRange` and value type is a point type with %Cartesian coordinates}
+ *     \cgalParamDefault{`CGAL::Identity_property_map<std::iterator_traits<PointRange::iterator>::value_type>`}
+ *   \cgalParamNEnd
  *   \cgalParamNBegin{stream_precision}
  *     \cgalParamDescription{a parameter used to set the precision (i.e. how many digits are generated) of the output stream}
  *     \cgalParamType{int}
diff --git a/Stream_support/include/CGAL/IO/OFF.h b/Stream_support/include/CGAL/IO/OFF.h
index e12e2494720..a7fc601ea49 100644
--- a/Stream_support/include/CGAL/IO/OFF.h
+++ b/Stream_support/include/CGAL/IO/OFF.h
@@ -268,9 +268,9 @@ bool read_OFF(const std::string& fname,
  *
  * \cgalNamedParamsBegin
  *   \cgalParamNBegin{point_map}
- *     \cgalParamDescription{a property map associating points with floating point coordinates to the elements of the point set `points`}
+ *     \cgalParamDescription{a property map associating points with %Cartesian coordinates to the elements of the point set `points`}
  *     \cgalParamType{a model of `ReadablePropertyMap` whose key type is the value type
- *                    of the iterator of `PointRange` and value type is a point type with floating point coordinates}
+ *                    of the iterator of `PointRange` and value type is a point type with %Cartesian coordinates}
  *     \cgalParamDefault{`CGAL::Identity_property_map<std::iterator_traits<PointRange::iterator>::value_type>`}
  *   \cgalParamNEnd
  *   \cgalParamNBegin{stream_precision}
@@ -315,9 +315,9 @@ bool write_OFF(std::ostream& os,
  *
  * \cgalNamedParamsBegin
  *   \cgalParamNBegin{point_map}
- *     \cgalParamDescription{a property map associating points with floating point coordinates to the elements of the point set `points`}
+ *     \cgalParamDescription{a property map associating points with %Cartesian coordinates to the elements of the point set `points`}
  *     \cgalParamType{a model of `ReadablePropertyMap` whose key type is the value type
- *                    of the iterator of `PointRange` and value type is a point type with floating point coordinates}
+ *                    of the iterator of `PointRange` and value type is a point type with %Cartesian coordinates}
  *     \cgalParamDefault{`CGAL::Identity_property_map<geom_traits::Point_3>`}
  *   \cgalParamNEnd
  *   \cgalParamNBegin{stream_precision}
diff --git a/Stream_support/include/CGAL/IO/STL.h b/Stream_support/include/CGAL/IO/STL.h
index dfa3ecded7e..06929db9ccf 100644
--- a/Stream_support/include/CGAL/IO/STL.h
+++ b/Stream_support/include/CGAL/IO/STL.h
@@ -17,6 +17,9 @@
 
 #include <CGAL/IO/STL/STL_reader.h>
 #include <CGAL/IO/helpers.h>
+#include <CGAL/Cartesian_converter.h>
+#include <CGAL/Simple_cartesian.h>
+
 
 #include <CGAL/Named_function_parameters.h>
 #include <CGAL/boost/graph/named_params_helper.h>
@@ -296,7 +299,6 @@ bool write_STL(std::ostream& os,
 
   typedef typename boost::property_traits<PointMap>::value_type             Point;
   typedef typename CGAL::Kernel_traits<Point>::Kernel                       K;
-  typedef typename K::Vector_3                                              Vector_3;
 
   K k = choose_parameter<K>(get_parameter(np, internal_np::geom_traits));
 
@@ -305,6 +307,11 @@ bool write_STL(std::ostream& os,
 
   set_stream_precision_from_NP(os, np);
 
+  typedef Simple_cartesian<double> SC;
+  typedef typename SC::Point_3  Point_3;
+  typedef typename SC::Vector_3 Vector_3;
+  Cartesian_converter<Kernel,SC> conv;
+
   if(get_mode(os) == BINARY)
   {
     os << "FileType: Binary                                                                ";
@@ -317,12 +324,16 @@ bool write_STL(std::ostream& os,
       const Point& q = get(point_map, points[face[1]]);
       const Point& r = get(point_map, points[face[2]]);
 
-      const Vector_3 n = collinear(p,q,r) ? Vector_3(1,0,0) : unit_normal(p,q,r);
+      Point_3 pp = conv(p);
+      Point_3 qq = conv(q);
+      Point_3 rr = conv(r);
 
-      const float coords[12] = { static_cast<float>(n.x()), static_cast<float>(n.y()), static_cast<float>(n.z()),
-                                 static_cast<float>(p.x()), static_cast<float>(p.y()), static_cast<float>(p.z()),
-                                 static_cast<float>(q.x()), static_cast<float>(q.y()), static_cast<float>(q.z()),
-                                 static_cast<float>(r.x()), static_cast<float>(r.y()), static_cast<float>(r.z()) };
+      const Vector_3 nn = collinear(pp,qq,rr) ? Vector_3(1,0,0) : unit_normal(pp,qq,rr);
+
+      const float coords[12] = { static_cast<float>(nn.x()), static_cast<float>(nn.y()), static_cast<float>(nn.z()),
+                                 static_cast<float>(pp.x()), static_cast<float>(pp.y()), static_cast<float>(pp.z()),
+                                 static_cast<float>(qq.x()), static_cast<float>(qq.y()), static_cast<float>(qq.z()),
+                                 static_cast<float>(rr.x()), static_cast<float>(rr.y()), static_cast<float>(rr.z()) };
 
       for(int i=0; i<12; ++i)
         os.write(reinterpret_cast<const char *>(&coords[i]), sizeof(coords[i]));
@@ -338,11 +349,15 @@ bool write_STL(std::ostream& os,
       const Point& q = get(point_map, points[face[1]]);
       const Point& r = get(point_map, points[face[2]]);
 
-      const Vector_3 n = internal::construct_normal_of_STL_face(p, q, r, k);
-      os << "facet normal " << n << "\nouter loop\n";
-      os << "vertex " << p << "\n";
-      os << "vertex " << q << "\n";
-      os << "vertex " << r << "\n";
+      Point_3 pp = conv(p);
+      Point_3 qq = conv(q);
+      Point_3 rr = conv(r);
+
+      const Vector_3 nn = conv(internal::construct_normal_of_STL_face(p, q, r, k));
+      os << "facet normal " << nn << "\nouter loop\n";
+      os << "vertex " << pp << "\n";
+      os << "vertex " << qq << "\n";
+      os << "vertex " << rr << "\n";
       os << "endloop\nendfacet\n";
     }
     os << "endsolid"<<std::endl;
diff --git a/Stream_support/test/Stream_support/issue_9071.cpp b/Stream_support/test/Stream_support/issue_9071.cpp
index 94b23c4581d..271dff3a6b2 100644
--- a/Stream_support/test/Stream_support/issue_9071.cpp
+++ b/Stream_support/test/Stream_support/issue_9071.cpp
@@ -11,7 +11,6 @@ using Epick = CGAL::Exact_predicates_inexact_constructions_kernel;
 int main() {
   std::vector<Kernel::Point_3> points;
   std::vector<std::array<std::size_t, 3>> polygons;
-  auto pm = CGAL::make_cartesian_converter_property_map<Epick::Point_3>(CGAL::make_identity_property_map(Kernel::Point_3()));
-  CGAL::IO::write_polygon_soup("xxx.off", points, polygons, CGAL::parameters::stream_precision(17).point_map(pm));
+  CGAL::IO::write_polygon_soup("xxx.off", points, polygons, CGAL::parameters::stream_precision(17));
   return 0;
 }