diff --git a/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Hyperbolic_triangulation_2.txt b/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Hyperbolic_triangulation_2.txt
index 9be7ec92ea9..b17e1d24b38 100644
--- a/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Hyperbolic_triangulation_2.txt
+++ b/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Hyperbolic_triangulation_2.txt
@@ -9,7 +9,7 @@ namespace CGAL {
\anchor chapterHTriangulation2
\cgalAutoToc
-\author Mikhail Bogdanov, and Iordan Iordanov, and Monique Teillaud
+\author Mikhail Bogdanov, Iordan Iordanov, and Monique Teillaud
@@ -46,22 +46,8 @@ As hyperbolic circles coincide with Euclidean circles contained in the
unit disk, the combinatorial structure of the hyperbolic Delaunay
triangulation of a set \f$\mathcal P\f$ of points in \f$\mathbb H^2\f$
is a subset of the Euclidean Delaunay triangulation of \f$\mathcal
-P\f$. Of course, the hyperbolic and Euclidean geometric embeddings of a
-given Delaunay face are different. See
-\cgalFigureRef{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}.
-
-\cgalFigureAnchor{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}
-
-
-
-\cgalFigureCaptionBegin{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}
-Comparison of the Euclidean (green) and hyperbolic (black) Delaunay triangulations
-of a given set of points in the unit disk. Note that only the colored faces
-are faces of the hyperbolic Delaunay triangulation.
-\cgalFigureCaptionEnd
-
-More precisely, the hyperbolic Delaunay triangulation of \f$\mathcal
-P\f$ is a connected simplicial complex. It only
+P\f$. More precisely, the hyperbolic Delaunay triangulation of \f$\mathcal
+P\f$ is a connected simplicial complex that only
contains the simplices of the Euclidean Delaunay triangulation that
are hyperbolic:
@@ -72,6 +58,20 @@ are hyperbolic:
P\f$) passing through its endpoints is contained in \f$\mathbb
H^2\f$.
+See \cgalFigureRef{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}.
+
+\cgalFigureAnchor{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}
+
+
+
+\cgalFigureCaptionBegin{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}
+Comparison of the Euclidean (green) and hyperbolic (black) Delaunay triangulations
+of a given set of points in the unit disk. Only the colored faces
+are faces of the hyperbolic Delaunay triangulation. The hyperbolic and Euclidean geometric embeddings of a
+Delaunay face that exists in both triangulations are different.
+\cgalFigureCaptionEnd
+
+
In the Euclidean Delaunay triangulation, there is a bijection between
non-hyperbolic faces and non-hyperbolic edges
\cgalCite{cgal:bdt-hdcvd-14}. See
@@ -91,7 +91,7 @@ as no empty circle through its endpoints is contained in
\section HT2_Software_design Software Design
From what was said above, it is natural that the class
`Hyperbolic_Delaunay_triangulation_2` privately inherits from the class
-`Delaunay_triangulation_2`. So, users are encouraged to look at the chapter
+`Delaunay_triangulation_2`. So, users are encouraged to look at Chapter
\ref Chapter_2D_Triangulations "2D Triangulation" of the CGAL manual to
know more in particular about the representation of triangulations in
CGAL and the flexibility of the design.