diff --git a/Frechet_distance/doc/Frechet_distance/Concepts/FrechetDistanceTraits.h b/Frechet_distance/doc/Frechet_distance/Concepts/FrechetDistanceTraits.h
index 32864e89cae6..cc2b50d5b9f4 100644
--- a/Frechet_distance/doc/Frechet_distance/Concepts/FrechetDistanceTraits.h
+++ b/Frechet_distance/doc/Frechet_distance/Concepts/FrechetDistanceTraits.h
@@ -20,9 +20,9 @@ class FrechetDistanceTraits {
 /// @{
 
 /*!
-Dimension type, being an instance of `CGAL::Dimension_tag`.
+Dimension type with the ambient dimension `d`.
 */
-using Dimension = unspecified_type;
+using Dimension = CGAL::Dimension_tag<d>;
 
 /*!
 Point type.
@@ -30,7 +30,7 @@ Point type.
 using Point_d = unspecified_type;
 
 /*!
-The number type of the %Cartesian coordinates of types `Point_d`.
+The number type of the %Cartesian coordinates of type `Point_d`.
 For a given `FT n`, `to_interval(n)` must be a valid expression and it must
 return an interval containing `n`, represented by a `std::pair<double, double>`.
 */
diff --git a/Frechet_distance/include/CGAL/Frechet_distance_traits_2.h b/Frechet_distance/include/CGAL/Frechet_distance_traits_2.h
index d0aae73fdaa3..d1e56f8133e3 100644
--- a/Frechet_distance/include/CGAL/Frechet_distance_traits_2.h
+++ b/Frechet_distance/include/CGAL/Frechet_distance_traits_2.h
@@ -26,15 +26,15 @@ namespace CGAL
  * \ingroup PkgFrechetDistanceTraits
  *
 * \cgalModels{FrechetDistanceTraits}
-* \tparam GT  geometric traits class
+* \tparam K  geometric traits class
 */
-template <class GT>
+template <class K>
 class Frechet_distance_traits_2
 {
 public:
   using Dimension = Dimension_tag<2>;
 
-  using Kernel = GT;
+  using Kernel = K;
   using FT = typename Kernel::FT;
   using Point_d = typename Kernel::Point_2;
   using Construct_bbox_d = typename Kernel::Construct_bbox_2;
diff --git a/Frechet_distance/include/CGAL/Frechet_distance_traits_3.h b/Frechet_distance/include/CGAL/Frechet_distance_traits_3.h
index d43fe8f368d7..75963ded5613 100644
--- a/Frechet_distance/include/CGAL/Frechet_distance_traits_3.h
+++ b/Frechet_distance/include/CGAL/Frechet_distance_traits_3.h
@@ -26,15 +26,15 @@ namespace CGAL
  * \ingroup PkgFrechetDistanceTraits
  *
 * \cgalModels{FrechetDistanceTraits}
-* \tparam GT  geometric traits class
+* \tparam K  geometric traits class
 */
-template <class GT>
+template <class K>
 class Frechet_distance_traits_3
 {
 public:
   using Dimension = Dimension_tag<3>;
 
-  using Kernel = GT;
+  using Kernel = K;
   using FT = typename Kernel::FT;
   using Point_d = typename Kernel::Point_3;
   using Construct_bbox_d = typename Kernel::Construct_bbox_3;
diff --git a/Frechet_distance/include/CGAL/Frechet_distance_traits_d.h b/Frechet_distance/include/CGAL/Frechet_distance_traits_d.h
index c435acdbd413..cef8461a6691 100644
--- a/Frechet_distance/include/CGAL/Frechet_distance_traits_d.h
+++ b/Frechet_distance/include/CGAL/Frechet_distance_traits_d.h
@@ -26,15 +26,15 @@ namespace CGAL
  * \ingroup PkgFrechetDistanceTraits
  *
 * \cgalModels{FrechetDistanceTraits}
-* \tparam GT  geometric traits class
+* \tparam K geometric traits class
 */
-template <class GT>
+template <class K>
 class Frechet_distance_traits_d
 {
 public:
-  using Dimension = Dimension_tag<GT::Dimension::value>;
+  using Dimension = Dimension_tag<K::Dimension::value>;
 
-  using Kernel = GT;
+  using Kernel = K;
   using FT = typename Kernel::FT;
   using Point_d = typename Kernel::Point_d;
   using Construct_bbox_d = typename Kernel::Construct_bbox_d;