diff --git a/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/Concepts/Periodic_2DelaunayTriangulationTraits_2.h b/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/Concepts/Periodic_2DelaunayTriangulationTraits_2.h
index ab34a9054ca..418a31eded5 100644
--- a/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/Concepts/Periodic_2DelaunayTriangulationTraits_2.h
+++ b/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/Concepts/Periodic_2DelaunayTriangulationTraits_2.h
@@ -6,10 +6,9 @@
 \cgalConcept
 
 The concept `Periodic_2DelaunayTriangulationTraits_2` is the first template parameter of the class
-`Periodic_2_Delaunay_triangulation_2`. It refines the concept
-`Periodic_2TriangulationTraits_2` and
-`DelaunayTriangulationTraits_2` from the \cgal \ref PkgTriangulation2 package. It redefines the
-geometric objects, predicates and constructions to work with
+`Periodic_2_Delaunay_triangulation_2`. It refines the concepts
+`Periodic_2TriangulationTraits_2` and `DelaunayTriangulationTraits_2`.
+It redefines the geometric objects, predicates and constructions to work with
 point-offset pairs. In most cases the offsets will be (0,0) and the
 predicates from `DelaunayTriangulationTraits_2` can be used
 directly. For efficiency reasons we maintain for each functor the
@@ -17,8 +16,9 @@ version without offsets.
 
 \cgalRefines ::DelaunayTriangulationTraits_2 and ::Periodic_2TriangulationTraits_2
 
-In addition to the requirements of the concept
-::Periodic_2TriangulationTraits_2, the concept ::Periodic_2DelaunayTriangulationTraits_2 provides a predicate to check the empty circle property. The
+In addition to the requirements of the concepts `Periodic_2TriangulationTraits_2`
+and `DelaunayTriangulationTraits_2`,
+the concept ::Periodic_2DelaunayTriangulationTraits_2 provides a predicate to check the empty circle property. The
 corresponding predicate type is called type ::Periodic_2DelaunayTriangulationTraits_2::Side_of_oriented_circle_2.
 
 The additional constructor object ::Periodic_2DelaunayTriangulationTraits_2::Construct_circumcenter_2 is
@@ -28,8 +28,6 @@ dual functions are called. The additional predicate type
 nearest_vertex(..) are issued.
 
 \cgalHasModel `CGAL::Periodic_2_Delaunay_triangulation_traits_2<Traits, Offset>`
-\cgalHasModel `CGAL::Periodic_2_triangulation_traits_2<Traits, Offset>`, which  implements
-additional the Delaunay predicates as well if the template parameter Traits is a model of `DelaunayTriangulationTraits_2`.
 
 \sa `DelaunayTriangulationTraits_2`
 */
diff --git a/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/Concepts/Periodic_2TriangulationTraits_2.h b/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/Concepts/Periodic_2TriangulationTraits_2.h
index a845d5fddd2..20d5c2a68ec 100644
--- a/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/Concepts/Periodic_2TriangulationTraits_2.h
+++ b/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/Concepts/Periodic_2TriangulationTraits_2.h
@@ -216,25 +216,17 @@ public:
 /// @}
 
 /// \name Creation
-/// Only a default constructor, copy constructor and an assignment
-/// operator are required. Note that further constructors can be
-/// provided.
 /// @{
 
   /*!
-  default constructor.
+  Default constructor.
   */
-  Periodic_2TriangulationTraits_2();
+  Periodic_2_triangulation_traits_2();
 
   /*!
-  Copy constructor
+  Copy constructor.
   */
-  Periodic_2TriangulationTraits_2(Periodic_2TriangulationTraits_2 gtr);
-
-  /*!
-  Assignment operator.
-  */
-  Periodic_2TriangulationTraits_2 operator=(Periodic_2TriangulationTraits_2 gtr);
+  Periodic_2_triangulation_traits_2(const Periodic_2_triangulation_traits_2& tr);
 
 /// @}
 
@@ -288,16 +280,14 @@ public:
 /// @{
 
   /*!
-  Sets the
-  fundamental domain. This is necessary to evaluate predicates
+  Sets the fundamental domain. This is necessary to evaluate predicates
   correctly.
   \pre `domain` represents a square.
   */
   void set_domain(Iso_rectangle_2 domain);
 
   /*!
-  Returns the
-  fundamental domain.
+  Returns the fundamental domain.
   */
   Iso_rectangle_2 get_domain() const;
 
diff --git a/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/Concepts/Periodic_2TriangulationVertexBase_2.h b/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/Concepts/Periodic_2TriangulationVertexBase_2.h
index 6be028ae5e9..8722dfa277e 100644
--- a/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/Concepts/Periodic_2TriangulationVertexBase_2.h
+++ b/Periodic_2_triangulation_2/doc/Periodic_2_triangulation_2/Concepts/Periodic_2TriangulationVertexBase_2.h
@@ -16,8 +16,6 @@ The storage of the offset is only needed when a triangulation is copied.
 
 \cgalRefines `TriangulationVertexBase_2`
 
-
-
 \cgalHasModel CGAL::Periodic_2_triangulation_vertex_base_2
 
 \sa `TriangulationDataStructure_2`