diff --git a/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Doxyfile.in b/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Doxyfile.in
index 9f9187d23b2..d163c185af0 100644
--- a/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Doxyfile.in
+++ b/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Doxyfile.in
@@ -12,7 +12,8 @@ HTML_EXTRA_FILES = 	${CGAL_PACKAGE_DOC_DIR}/fig/octagon_identification.svg \
 					${CGAL_PACKAGE_DOC_DIR}/fig/dt-construction.svg \
 					${CGAL_PACKAGE_DOC_DIR}/fig/periodic_face.svg \
 					${CGAL_PACKAGE_DOC_DIR}/fig/ds_cgal.svg \
-					${CGAL_PACKAGE_DOC_DIR}/fig/dummy-points.png
+					${CGAL_PACKAGE_DOC_DIR}/fig/dummy-points.png \
+					${CGAL_PACKAGE_DOC_DIR}/fig/non-triangulation.svg \
 
 HTML_EXTRA_STYLESHEET = ${CGAL_PACKAGE_DOC_DIR}/css/customstyle.css
 
diff --git a/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Periodic_4_hyperbolic_triangulation_2.txt b/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Periodic_4_hyperbolic_triangulation_2.txt
index cd3586bc24c..cecaa7ce518 100644
--- a/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Periodic_4_hyperbolic_triangulation_2.txt
+++ b/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Periodic_4_hyperbolic_triangulation_2.txt
@@ -237,6 +237,19 @@ Some point sets do not admit a triangulation of \f$\mathcal M\f$.
 For instance, a single point does not define a triangulation of \f$\mathcal M\f$, as the result
 would not be a simplicial complex.
 \cgalModifEnd
+
+\cgalFigureAnchor{P4HNonSimplicialExample}
+<center>
+  <img src="non-triangulation.svg" style="max-width:45%; width=45%; display: inline-block;"/>
+</center>
+\cgalFigureCaptionBegin{P4HNonSimplicialExample}
+  Example of a non-simplicial decomposition of the Bolza surface. Note that with the three 
+  points in the central octagon, we obtain a decomposition that is <b>not</b> a triangulation,
+  since it is non-simplicial. On the figure a few cycles of length 2 are shown in color. Such
+  cycles are double edges in the triangulation. Note also the pink edge between the two blue 
+  vertices: it corresponds to a loop on the surface.
+\cgalFigureCaptionEnd
+
 For this reason, we initialize a triangulation of \f$\mathcal M\f$ with a predetermined set of 
 14 points, called <i>dummy points</i>, whose triangulation in \f$\mathcal M\f$ is a simplicial 
 complex and has the empty circle property. The set of dummy points has been proposed in