diff --git a/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationDSFaceBase_2.h b/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationFaceBase_2.h
similarity index 79%
rename from Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationDSFaceBase_2.h
rename to Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationFaceBase_2.h
index 70db99e3321..66ac0ac653b 100644
--- a/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationDSFaceBase_2.h
+++ b/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationFaceBase_2.h
@@ -6,9 +6,9 @@
 \cgalConcept
 
 \cgalModifBegin
-\cgalRefines TriangulationDSFaceBase_2
+\cgalRefines TriangulationFaceBase_2
 
-A refinement of the concept `TriangulationDSFaceBase_2` that adds an interface for hyperbolic translations.
+A refinement of the concept `TriangulationFaceBase_2` that adds an interface for hyperbolic translations.
 \cgalModifEnd
 
 At the base level, a face stores handles to its incident vertices and to its neighboring faces. 
@@ -20,14 +20,14 @@ For periodic hyperbolic triangulations, the face base class needs to store three
 one for each vertex. Applying each translation to the point stored in the corresponding vertex produces 
 the canonical representative of the face in the hyperbolic plane.
 
-\cgalHasModel CGAL::Periodic_4_hyperbolic_triangulation_ds_face_base_2
+\cgalHasModel CGAL::Periodic_4_hyperbolic_triangulation_face_base_2
 
 \sa `TriangulationDataStructure_2`
-\sa `Periodic_4HyperbolicTriangulationDSVertexBase_2`
+\sa `Periodic_4HyperbolicTriangulationVertexBase_2`
 
 */
 
-class Periodic_4HyperbolicTriangulationDSFaceBase_2 
+class Periodic_4HyperbolicTriangulationFaceBase_2 
 {
 public:
 
@@ -47,12 +47,12 @@ public:
 		/*!
 		Default constructor.
 		*/
-		Periodic_4HyperbolicTriangulationDSFaceBase_2();
+		Periodic_4HyperbolicTriangulationFaceBase_2();
 
 		/*!
 		Creates a face with vertices `v0, v1` and `v1`.
 		*/
-		Periodic_4HyperbolicTriangulationDSFaceBase_2(
+		Periodic_4HyperbolicTriangulationFaceBase_2(
 			const Vertex_handle& v0, const Vertex_handle& v1,
 			const Vertex_handle& v2); 
 
@@ -60,7 +60,7 @@ public:
 		Creates a face with vertices `v0, v1` and `v1`, setting 
 		also neighborhood relations with `n0, n1` and `n2`.
 		*/
-		Periodic_4HyperbolicTriangulationDSFaceBase_2(
+		Periodic_4HyperbolicTriangulationFaceBase_2(
 			const Vertex_handle& v0, const Vertex_handle& v1,
 			const Vertex_handle& v2, const Face_handle&   n0,
 			const Face_handle&   n1, const Face_handle&   n2); 
@@ -88,7 +88,7 @@ public:
 			Changes the orientation of the face by exchanging `vertex(0)` with `vertex(1)`, 
 			`neighbor(0)` with `neighbor(1)`, and `translation(0)` with `translation(1)`.
 
-			\sa TriangulationDSFaceBase_2::reorient() 
+			\sa TriangulationFaceBase_2::reorient() 
 		*/
 		void reorient();
 
diff --git a/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationDSVertexBase_2.h b/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationVertexBase_2.h
similarity index 76%
rename from Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationDSVertexBase_2.h
rename to Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationVertexBase_2.h
index 7cd6d3378a9..940356e8af5 100644
--- a/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationDSVertexBase_2.h
+++ b/Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationVertexBase_2.h
@@ -6,9 +6,9 @@
 \cgalConcept
 
 \cgalModifBegin
-\cgalRefines TriangulationDSVertexBase_2
+\cgalRefines TriangulationVertexBase_2
 
-A refinement of the concept `TriangulationDSVertexBase_2` that adds an interface for hyperbolic translations.
+A refinement of the concept `TriangulationVertexBase_2` that adds an interface for hyperbolic translations.
 \cgalModifEnd
 
 For periodic hyperbolic triangulations, the vertex base class needs to temporarily store a hyperbolic 
@@ -18,15 +18,15 @@ A boolean flag indicates whether the face stores a translation or not. The value
 set when storing or removing a translation.
 \cgalModifEnd
 
-\cgalHasModel `CGAL::Periodic_4_hyperbolic_triangulation_ds_vertex_base_2`
+\cgalHasModel `CGAL::Periodic_4_hyperbolic_triangulation_vertex_base_2`
 
 \sa `TriangulationDataStructure_2`
-\sa `Periodic_4HyperbolicTriangulationDSFaceBase_2`
+\sa `Periodic_4HyperbolicTriangulationFaceBase_2`
 
 */
 
 
-class Periodic_4HyperbolicTriangulationDSVertexBase_2 {
+class Periodic_4HyperbolicTriangulationVertexBase_2 {
 public:
 
   /// \name Types
@@ -37,7 +37,7 @@ public:
     (note: was inheriting from `Vb`, which is not defined here)
   \cgalModifEnd
   */
-  typedef typename TriangulationDSVertexBase_2::Face_handle 		    
+  typedef typename TriangulationVertexBase_2::Face_handle 		    
                                                       Face_handle;
   
   /*!
@@ -62,22 +62,22 @@ public:
   /*!
     Default constructor.
   */
-	Periodic_4HyperbolicTriangulationDSVertexBase_2();
+	Periodic_4HyperbolicTriangulationVertexBase_2();
 
   /*!
     Construct a vertex that stores the point `p`.
   */
-	Periodic_4HyperbolicTriangulationDSVertexBase_2(const Point & p);
+	Periodic_4HyperbolicTriangulationVertexBase_2(const Point & p);
 
   /*!
     Constructs a vertex that stores the point `p` and is incident to the face `fh`.
   */
-  Periodic_4HyperbolicTriangulationDSVertexBase_2(const Point & p, Face_handle fh);
+  Periodic_4HyperbolicTriangulationVertexBase_2(const Point & p, Face_handle fh);
 
   /*!
     Constructs a vertex that is incident to the face `fh`.
   */
-	Periodic_4HyperbolicTriangulationDSVertexBase_2(const Face_handle& fh);
+	Periodic_4HyperbolicTriangulationVertexBase_2(const Face_handle& fh);
   /// @}