diff --git a/BGL/include/CGAL/boost/graph/parameters_interface.h b/BGL/include/CGAL/boost/graph/parameters_interface.h
index de168a93dfb..54f039ee345 100644
--- a/BGL/include/CGAL/boost/graph/parameters_interface.h
+++ b/BGL/include/CGAL/boost/graph/parameters_interface.h
@@ -103,6 +103,7 @@ CGAL_add_named_parameter(volume_threshold_t, volume_threshold, volume_threshold)
 CGAL_add_named_parameter(dry_run_t, dry_run, dry_run)
 CGAL_add_named_parameter(do_not_modify_t, do_not_modify, do_not_modify)
 CGAL_add_named_parameter(allow_self_intersections_t, allow_self_intersections, allow_self_intersections)
+CGAL_add_named_parameter(polyhedral_envelope_epsilon_t, polyhedral_envelope_epsilon, polyhedral_envelope_epsilon)
 
 // 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)
diff --git a/BGL/test/BGL/test_cgal_bgl_named_params.cpp b/BGL/test/BGL/test_cgal_bgl_named_params.cpp
index 18db63159e4..f7bf797a8da 100644
--- a/BGL/test/BGL/test_cgal_bgl_named_params.cpp
+++ b/BGL/test/BGL/test_cgal_bgl_named_params.cpp
@@ -99,6 +99,7 @@ void test(const NamedParameters& np)
   assert(get_parameter(np, CGAL::internal_np::do_simplify_border).v == 64);
   assert(get_parameter(np, CGAL::internal_np::do_not_modify).v == 65);
   assert(get_parameter(np, CGAL::internal_np::allow_self_intersections).v == 66);
+  assert(get_parameter(np, CGAL::internal_np::polyhedral_envelope_epsilon).v == 67);
   assert(get_parameter(np, CGAL::internal_np::maximum_number_of_faces).v == 78910);
 
     // Named parameters that we use in the package 'Surface Mesh Simplification'
@@ -188,6 +189,7 @@ void test(const NamedParameters& np)
   check_same_type<56>(get_parameter(np, CGAL::internal_np::use_safety_constraints));
   check_same_type<65>(get_parameter(np, CGAL::internal_np::do_not_modify));
   check_same_type<66>(get_parameter(np, CGAL::internal_np::allow_self_intersections));
+  check_same_type<67>(get_parameter(np, CGAL::internal_np::polyhedral_envelope_epsilon));
 
   check_same_type<12340>(get_parameter(np, CGAL::internal_np::do_self_intersection_tests));
   check_same_type<12341>(get_parameter(np, CGAL::internal_np::do_orientation_tests));
@@ -363,6 +365,7 @@ int main()
                          .do_simplify_border(A<64>(64))
                          .do_not_modify(A<65>(65))
                          .allow_self_intersections(A<66>(66))
+                         .polyhedral_envelope_epsilon(A<67>(67))
                          .point_map(A<9000>(9000))
                          .query_point_map(A<9001>(9001))
                          .normal_map(A<9002>(9002))