diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h
index b9701de8c03..813c6a3ef8e 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h
@@ -278,9 +278,11 @@ namespace CGAL {
     *       axis-aligned bounding box.}
     *     \cgalParamDefault{1.}
     *   \cgalParamNEnd
-    *   \cgalParamNBegin{triangulate_bbox}
-    *     \cgalParamDescription{a boolean used to specify if the bounding box should be triangulated or not.}
-    *     \cgalParamDefault{true}
+    *   \cgalParamNBegin{do_not_triangulate_faces}
+    *     \cgalParamDescription{a boolean used to specify if the bounding box faces
+    *       should be triangulated or not.
+    *       The default value is `false`, and faces are triangulated.}
+    *     \cgalParamDefault{false}
     *   \cgalParamNEnd
     *   \cgalParamNBegin{geom_traits}
     *     \cgalParamDescription{an instance of a geometric traits class providing the functor `Construct_bbox_3`,
@@ -306,7 +308,8 @@ namespace CGAL {
       using Vector_3 = typename GT::Vector_3;
 
       double factor = choose_parameter(get_parameter(np, internal_np::bbox_scaling), 1.);
-      bool triangulate = choose_parameter(get_parameter(np, internal_np::triangulate_bbox), true);
+      bool dont_triangulate = choose_parameter(
+        get_parameter(np, internal_np::do_not_triangulate_faces), false);
 
       Iso_cuboid_3 bb(CGAL::Polygon_mesh_processing::bbox(pmesh));
       Point_3 bb_center(0.5 * (bb.xmax() + bb.xmin()),
@@ -321,7 +324,7 @@ namespace CGAL {
                             bbext[4], bbext[5], bbext[6], bbext[7],
                             bbox_mesh);
 
-      if(triangulate)
+      if(!dont_triangulate)
         CGAL::Polygon_mesh_processing::triangulate_faces(bbox_mesh);
 
       CGAL::copy_face_graph(bbox_mesh, pmesh,
diff --git a/Polyhedron/demo/Polyhedron/Plugins/PMP/Repair_polyhedron_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/PMP/Repair_polyhedron_plugin.cpp
index aa54e0679b7..496b998a97a 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/PMP/Repair_polyhedron_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/PMP/Repair_polyhedron_plugin.cpp
@@ -395,7 +395,7 @@ void Polyhedron_demo_repair_polyhedron_plugin::on_actionAddBbox_triggered(Scene_
     const double scaling = ui.bbox_scaling->value();
     CGAL::Polygon_mesh_processing::add_bbox(*poly_item->face_graph(),
       CGAL::parameters::bbox_scaling(scaling).
-                        triangulate_bbox(ui.triangulate_bbox->isChecked()));
+      do_not_triangulate_faces(!ui.triangulate_bbox->isChecked()));
 
     poly_item->invalidateOpenGLBuffers();
     Q_EMIT poly_item->itemChanged();
diff --git a/STL_Extension/include/CGAL/STL_Extension/internal/parameters_interface.h b/STL_Extension/include/CGAL/STL_Extension/internal/parameters_interface.h
index c5c143399d6..7f84dd628e3 100644
--- a/STL_Extension/include/CGAL/STL_Extension/internal/parameters_interface.h
+++ b/STL_Extension/include/CGAL/STL_Extension/internal/parameters_interface.h
@@ -164,7 +164,6 @@ CGAL_add_named_parameter(region_primitive_map_t, region_primitive_map, region_pr
 CGAL_add_named_parameter(postprocess_regions_t, postprocess_regions, postprocess_regions)
 CGAL_add_named_parameter(sizing_function_t, sizing_function, sizing_function)
 CGAL_add_named_parameter(bbox_scaling_t, bbox_scaling, bbox_scaling)
-CGAL_add_named_parameter(triangulate_bbox_t, triangulate_bbox, triangulate_bbox)
 
 // List of named parameters that we use in the package 'Surface Mesh Simplification'
 CGAL_add_named_parameter(get_cost_policy_t, get_cost_policy, get_cost)