diff --git a/Surface_mesh/doc/Surface_mesh/Surface_mesh.txt b/Surface_mesh/doc/Surface_mesh/Surface_mesh.txt
index 754f49ac762..601649f4e49 100644
--- a/Surface_mesh/doc/Surface_mesh/Surface_mesh.txt
+++ b/Surface_mesh/doc/Surface_mesh/Surface_mesh.txt
@@ -53,7 +53,9 @@ elements can be added and removed to the `Surface_mesh` through a
 set of low-level functions which do not maintain connectivity. One
 exception is `Surface_mesh::add_face()`, which tries to add a new
 face to the mesh (defined by a sequence of vertices), and fails if the
-operation is not topologically valid.
+operation is not topologically valid. In that case, the returned
+`Face_index` is `Surface_mesh::null_face()`.
+
 
 \code
 typedef Surface_mesh<Point> Mesh;
@@ -73,6 +75,13 @@ do not have member functions to access connectivity or properties.
 The functions of the `Surface_mesh` instance from which
 they were created must be used to obtain this information.
 
+\subsection usage_example Example
+
+The following example shows how to create a very simple `Surface_mesh`
+by adding 2 faces, and how to check that a face is correctly added
+to the mesh.
+
+\cgalExample{Surface_mesh/sm_check_wrong_orientation.cpp}
 \section sectionSurfaceMeshConnectivity Connectivity 
 
 A surface mesh is an edge-centered data structure capable of
diff --git a/Surface_mesh/doc/Surface_mesh/examples.txt b/Surface_mesh/doc/Surface_mesh/examples.txt
index b19e4dfa646..0e21e9bcfec 100644
--- a/Surface_mesh/doc/Surface_mesh/examples.txt
+++ b/Surface_mesh/doc/Surface_mesh/examples.txt
@@ -1,4 +1,5 @@
 /*!
+\example Surface_mesh/sm_check_wrong_orientation.cpp
 \example Surface_mesh/sm_iterators.cpp
 \example Surface_mesh/sm_circulators.cpp
 \example Surface_mesh/sm_properties.cpp
diff --git a/Surface_mesh/examples/Surface_mesh/sm_check_wrong_orientation.cpp b/Surface_mesh/examples/Surface_mesh/sm_check_wrong_orientation.cpp
index 972e98878c2..b438f393ea3 100644
--- a/Surface_mesh/examples/Surface_mesh/sm_check_wrong_orientation.cpp
+++ b/Surface_mesh/examples/Surface_mesh/sm_check_wrong_orientation.cpp
@@ -1,6 +1,3 @@
-#include <vector>
-
-
 #include <CGAL/Simple_cartesian.h>
 #include <CGAL/Surface_mesh.h>