diff --git a/Orthtree/doc/Orthtree/Concepts/OrthtreeTraits.h b/Orthtree/doc/Orthtree/Concepts/OrthtreeTraits.h
index 471ada54c71..f6791c13c78 100644
--- a/Orthtree/doc/Orthtree/Concepts/OrthtreeTraits.h
+++ b/Orthtree/doc/Orthtree/Concepts/OrthtreeTraits.h
@@ -8,7 +8,7 @@
   \cgalHasModelsBegin
   \cgalHasModels{CGAL::Orthtree_traits_point<GeomTraits, PointRange, PointMap, dimension >}
   \cgalHasModels{CGAL::Orthtree_traits_face_graph<PolygonMesh, VPM>}
-  \cgalHasModels{CGAL::Orthtree_traits_base_for_dimension< K, dimension >}
+  \cgalHasModels{CGAL::Orthtree_traits_base< K, dimension >}
   \cgalHasModelsEnd
 */
 class OrthtreeTraits
diff --git a/Orthtree/examples/Orthtree/quadtree_build_manually.cpp b/Orthtree/examples/Orthtree/quadtree_build_manually.cpp
index 601917bf3c9..2e38f406c38 100644
--- a/Orthtree/examples/Orthtree/quadtree_build_manually.cpp
+++ b/Orthtree/examples/Orthtree/quadtree_build_manually.cpp
@@ -4,7 +4,7 @@
 #include <CGAL/Dimension.h>
 
 #include <CGAL/Orthtree.h>
-#include <CGAL/Orthtree_traits_base_for_dimension.h>
+#include <CGAL/Orthtree_traits_base.h>
 
 using Kernel = CGAL::Simple_cartesian<double>;
 
@@ -14,7 +14,7 @@ struct empty_type {
 };
 
 template <typename K, int dimension>
-struct Orthtree_traits_empty : public Orthtree_traits_base_for_dimension<K, dimension> {
+struct Orthtree_traits_empty : public Orthtree_traits_base<K, dimension> {
 
   using Self = Orthtree_traits_empty<K, dimension>;
   using Tree = Orthtree<Self>;
diff --git a/Orthtree/include/CGAL/Orthtree_traits_base_for_dimension.h b/Orthtree/include/CGAL/Orthtree_traits_base.h
similarity index 85%
rename from Orthtree/include/CGAL/Orthtree_traits_base_for_dimension.h
rename to Orthtree/include/CGAL/Orthtree_traits_base.h
index 88043d53cdf..a97f0f74101 100644
--- a/Orthtree/include/CGAL/Orthtree_traits_base_for_dimension.h
+++ b/Orthtree/include/CGAL/Orthtree_traits_base.h
@@ -9,8 +9,8 @@
 //
 // Author(s)     : Jackson Campolattaro
 
-#ifndef ORTHTREE_ORTHTREE_TRAITS_BASE_FOR_DIMENSION_H
-#define ORTHTREE_ORTHTREE_TRAITS_BASE_FOR_DIMENSION_H
+#ifndef ORTHTREE_ORTHTREE_TRAITS_BASE_H
+#define ORTHTREE_ORTHTREE_TRAITS_BASE_H
 
 #include <CGAL/license/Orthtree.h>
 
@@ -24,7 +24,7 @@ namespace CGAL {
 /*!
   \ingroup PkgOrthtreeTraits
 
-  The class `Orthtree_traits_base_for_dimension` is a base class providing common choices for types and functors.
+  The class `Orthtree_traits_base` is a base class providing common choices for types and functors.
   The base class is extended by `CGAL::Orthtree_traits_point<GeomTraits, PointRange, PointMap, dimension>` and by `CGAL::Orthtree_traits_face_graph<PolygonMesh, VertexPointMap>`.
 
   \tparam K a model of `Kernel`.
@@ -35,7 +35,7 @@ namespace CGAL {
 */
 
 template <typename K, int dim>
-struct Orthtree_traits_base_for_dimension {
+struct Orthtree_traits_base {
   /// \name Types
   /// @{
   using Node_index = std::size_t;
@@ -97,16 +97,10 @@ struct Orthtree_traits_base_for_dimension {
       return Point_d{static_cast<int>(args_list.size()), args_list.begin(), args_list.end()};
     };
   }
-
-  auto locate_halfspace_object() const {
-    return [](const FT& a, const FT& b) -> bool {
-      return a < b;
-      };
-  }
 };
 
 template <typename K>
-struct Orthtree_traits_base_for_dimension<K, 2> {
+struct Orthtree_traits_base<K, 2> {
   using Node_index = std::size_t;
   using Kernel = K;
   static constexpr int dimension = 2;
@@ -128,16 +122,10 @@ struct Orthtree_traits_base_for_dimension<K, 2> {
       return {x, y};
     };
   }
-
-  auto locate_halfspace_object() const {
-    return [](const FT& a, const FT& b) -> bool {
-      return a < b;
-      };
-  }
 };
 
 template <typename K>
-struct Orthtree_traits_base_for_dimension<K, 3> {
+struct Orthtree_traits_base<K, 3> {
   using Node_index = std::size_t;
   using Kernel = K;
   static constexpr int dimension = 3;
@@ -172,14 +160,8 @@ struct Orthtree_traits_base_for_dimension<K, 3> {
       return {x, y, z};
     };
   }
-
-  auto locate_halfspace_object() const {
-    return [](const FT& a, const FT& b) -> bool {
-      return a < b;
-      };
-  }
 };
 
 }
 
-#endif //ORTHTREE_ORTHTREE_TRAITS_BASE_FOR_DIMENSION_H
+#endif //ORTHTREE_ORTHTREE_TRAITS_BASE_H
diff --git a/Orthtree/include/CGAL/Orthtree_traits_face_graph.h b/Orthtree/include/CGAL/Orthtree_traits_face_graph.h
index a0773582dc9..80fed2fbe95 100644
--- a/Orthtree/include/CGAL/Orthtree_traits_face_graph.h
+++ b/Orthtree/include/CGAL/Orthtree_traits_face_graph.h
@@ -15,7 +15,7 @@
 
 #include <CGAL/license/Orthtree.h>
 
-#include <CGAL/Orthtree_traits_base_for_dimension.h>
+#include <CGAL/Orthtree_traits_base.h>
 
 #include <boost/graph/graph_traits.hpp>
 #include <CGAL/Dimension.h>
@@ -38,7 +38,7 @@ to which the minimal extend of a node should be provided.
 \cgalModels{OrthtreeTraits}
 */
 template <class TriangleMesh, class VertexPointMap>
-struct Orthtree_traits_face_graph : public Orthtree_traits_base_for_dimension<
+struct Orthtree_traits_face_graph : public Orthtree_traits_base<
   typename Kernel_traits<typename boost::property_traits<VertexPointMap>::value_type>::type, 3 > {
 
   Orthtree_traits_face_graph(const TriangleMesh& pm, VertexPointMap vpm)
@@ -47,7 +47,7 @@ struct Orthtree_traits_face_graph : public Orthtree_traits_base_for_dimension<
   /// \name Types
   /// @{
 
-  using Base = Orthtree_traits_base_for_dimension<
+  using Base = Orthtree_traits_base<
   typename Kernel_traits<typename boost::property_traits<VertexPointMap>::value_type>::type, 3 >;
   using Node_index = typename Base::Node_index;
   using Self = Orthtree_traits_face_graph<TriangleMesh, VertexPointMap>;
diff --git a/Orthtree/include/CGAL/Orthtree_traits_point.h b/Orthtree/include/CGAL/Orthtree_traits_point.h
index 4aa733a9660..0e6c3f98d84 100644
--- a/Orthtree/include/CGAL/Orthtree_traits_point.h
+++ b/Orthtree/include/CGAL/Orthtree_traits_point.h
@@ -19,7 +19,7 @@
 #include <CGAL/Point_set_2.h>
 #include <CGAL/Orthtree/Cartesian_ranges.h>
 
-#include <CGAL/Orthtree_traits_base_for_dimension.h>
+#include <CGAL/Orthtree_traits_base.h>
 
 namespace CGAL {
 
@@ -74,7 +74,7 @@ void reassign_points(
   \cgalModels{OrthtreeTraits}
   \sa `CGAL::Octree`
   \sa `CGAL::Quadtree`
-  \sa `CGAL::Orthtree_traits_base_for_dimension<GeomTraits, DimensionTag>`
+  \sa `CGAL::Orthtree_traits_base<GeomTraits, DimensionTag>`
 */
 template <
   typename GeomTraits,
@@ -85,14 +85,14 @@ template <
     GeomTraits
   >::value
 >
-struct Orthtree_traits_point : public Orthtree_traits_base_for_dimension<GeomTraits, dimension> {
+struct Orthtree_traits_point : public Orthtree_traits_base<GeomTraits, dimension> {
 public:
   /// \name Types
   /// @{
   using Node_data = boost::iterator_range<typename PointRange::iterator>;
   /// @}
 
-  using Base = Orthtree_traits_base_for_dimension<GeomTraits, dimension>;
+  using Base = Orthtree_traits_base<GeomTraits, dimension>;
   using Self = Orthtree_traits_point<GeomTraits, PointRange, PointMap, dimension>;
   using Tree = Orthtree<Self>;