diff --git a/Periodic_3_mesh_3/include/CGAL/make_periodic_3_mesh_3.h b/Periodic_3_mesh_3/include/CGAL/make_periodic_3_mesh_3.h
index 2c42a1b9800..570d1fb610b 100644
--- a/Periodic_3_mesh_3/include/CGAL/make_periodic_3_mesh_3.h
+++ b/Periodic_3_mesh_3/include/CGAL/make_periodic_3_mesh_3.h
@@ -312,7 +312,7 @@ struct C3t3_initializer<C3T3, MeshDomain, MeshCriteria, true, CGAL::Tag_true>
  * \sa `odt_optimize_mesh_3()`
  */
 template<typename C3T3, typename MeshDomain, typename MeshCriteria, typename CGAL_NP_TEMPLATE_PARAMETERS>
-C3T3 make_periodic_3_mesh_3(MeshDomain& domain, MeshCriteria& criteria, const CGAL_NP_CLASS& np = parameters::default_values())
+C3T3 make_periodic_3_mesh_3(const MeshDomain& domain, const MeshCriteria& criteria, const CGAL_NP_CLASS& np = parameters::default_values())
 {
   using parameters::choose_parameter;
   using parameters::get_parameter;
@@ -339,7 +339,7 @@ template<typename C3T3, typename MeshDomain, typename MeshCriteria,
          typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_1,
          typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_2,
          typename ... NP>
-C3T3 make_periodic_3_mesh_3(MeshDomain& domain, MeshCriteria& criteria,
+C3T3 make_periodic_3_mesh_3(const MeshDomain& domain, const MeshCriteria& criteria,
                             const CGAL_NP_CLASS_1&  np1,
                             const CGAL_NP_CLASS_2&  np2,
                             const NP& ... nps)
diff --git a/Periodic_3_mesh_3/include/CGAL/optimize_periodic_3_mesh_3.h b/Periodic_3_mesh_3/include/CGAL/optimize_periodic_3_mesh_3.h
index 0a7c1e5ef4c..b9ed2f3a327 100644
--- a/Periodic_3_mesh_3/include/CGAL/optimize_periodic_3_mesh_3.h
+++ b/Periodic_3_mesh_3/include/CGAL/optimize_periodic_3_mesh_3.h
@@ -34,7 +34,7 @@ namespace CGAL {
  * Further information can be found in the documentation of the function `perturb_mesh_3()`.
  */
 template<typename C3T3, typename MeshDomain, typename CGAL_NP_TEMPLATE_PARAMETERS>
-Mesh_optimization_return_code perturb_periodic_3_mesh_3(C3T3& c3t3, MeshDomain& domain, const CGAL_NP_CLASS& np = parameters::default_values())
+Mesh_optimization_return_code perturb_periodic_3_mesh_3(C3T3& c3t3, const MeshDomain& domain, const CGAL_NP_CLASS& np = parameters::default_values())
 {
   using parameters::choose_parameter;
   using parameters::get_parameter;
@@ -50,7 +50,7 @@ template<typename C3T3, typename MeshDomain,
          typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_1,
          typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_2,
          typename ... NP>
-Mesh_optimization_return_code perturb_periodic_3_mesh_3(C3T3& c3t3, MeshDomain& domain,
+Mesh_optimization_return_code perturb_periodic_3_mesh_3(C3T3& c3t3, const MeshDomain& domain,
                                                         const CGAL_NP_CLASS_1&  np1,
                                                         const CGAL_NP_CLASS_2&  np2,
                                                         const NP& ... nps)
@@ -131,7 +131,7 @@ Mesh_optimization_return_code exude_periodic_3_mesh_3(const CGAL_NP_CLASS_1&  np
  * Further information can be found in the documentation of the function `odt_optimize_mesh_3()`.
  */
 template<typename C3T3,typename MeshDomain,typename CGAL_NP_TEMPLATE_PARAMETERS>
-Mesh_optimization_return_code odt_optimize_periodic_3_mesh_3(C3T3& c3t3, MeshDomain& domain, const CGAL_NP_CLASS& np = parameters::default_values())
+Mesh_optimization_return_code odt_optimize_periodic_3_mesh_3(C3T3& c3t3, const MeshDomain& domain, const CGAL_NP_CLASS& np = parameters::default_values())
 {
   using parameters::choose_parameter;
   using parameters::get_parameter;
@@ -148,7 +148,7 @@ template<typename C3T3, typename MeshDomain,
          typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_1,
          typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_2,
          typename ... NP>
-Mesh_optimization_return_code odt_optimize_periodic_3_mesh_3(C3T3& c3t3, MeshDomain& domain,
+Mesh_optimization_return_code odt_optimize_periodic_3_mesh_3(C3T3& c3t3, const MeshDomain& domain,
                                                              const CGAL_NP_CLASS_1&  np1,
                                                              const CGAL_NP_CLASS_2&  np2,
                                                              const NP& ... nps)
@@ -180,7 +180,7 @@ Mesh_optimization_return_code odt_optimize_periodic_3_mesh_3(const CGAL_NP_CLASS
  * \note This function requires the \ref thirdpartyEigen library.
 */
 template<typename C3T3, typename MeshDomain, typename CGAL_NP_TEMPLATE_PARAMETERS>
-Mesh_optimization_return_code lloyd_optimize_periodic_3_mesh_3(C3T3& c3t3, MeshDomain& domain,const CGAL_NP_CLASS& np = parameters::default_values())
+Mesh_optimization_return_code lloyd_optimize_periodic_3_mesh_3(C3T3& c3t3, const MeshDomain& domain,const CGAL_NP_CLASS& np = parameters::default_values())
 {
   using parameters::choose_parameter;
   using parameters::get_parameter;
@@ -197,7 +197,7 @@ template<typename C3T3, typename MeshDomain,
          typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_1,
          typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_2,
          typename ... NP>
-Mesh_optimization_return_code lloyd_optimize_periodic_3_mesh_3(C3T3& c3t3,MeshDomain& domain,
+Mesh_optimization_return_code lloyd_optimize_periodic_3_mesh_3(C3T3& c3t3, const MeshDomain& domain,
                                                                const CGAL_NP_CLASS_1&  np1,
                                                                const CGAL_NP_CLASS_2&  np2,
                                                                const NP& ... nps)
diff --git a/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h b/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h
index f013a73e9d8..5197b36d752 100644
--- a/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h
+++ b/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h
@@ -298,7 +298,7 @@ void project_points(C3T3& c3t3,
  * \sa `odt_optimize_periodic_3_mesh_3()`
  */
 template<typename C3T3, typename MeshDomain, typename MeshCriteria, typename CGAL_NP_TEMPLATE_PARAMETERS>
-void refine_periodic_3_mesh_3(C3T3& c3t3, MeshDomain& domain, MeshCriteria& criteria, const CGAL_NP_CLASS& np = parameters::default_values())
+void refine_periodic_3_mesh_3(C3T3& c3t3, const MeshDomain& domain, const MeshCriteria& criteria, const CGAL_NP_CLASS& np = parameters::default_values())
 {
   using parameters::choose_parameter;
   using parameters::get_parameter;
@@ -328,7 +328,7 @@ template<typename C3T3, typename MeshDomain, typename MeshCriteria,
          typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_1,
          typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_2,
          typename ... NP>
-void refine_periodic_3_mesh_3(C3T3& c3t3, MeshDomain& domain, MeshCriteria& criteria,
+void refine_periodic_3_mesh_3(C3T3& c3t3, const MeshDomain& domain, const MeshCriteria& criteria,
                               const CGAL_NP_CLASS_1&  np1,
                               const CGAL_NP_CLASS_2&  np2,
                               const NP& ... nps)