diff --git a/Mesh_3/doc/Mesh_3/CGAL/IO/File_medit.h b/Mesh_3/doc/Mesh_3/CGAL/IO/File_medit.h
index 696e7b3e9cd..e50566add7b 100644
--- a/Mesh_3/doc/Mesh_3/CGAL/IO/File_medit.h
+++ b/Mesh_3/doc/Mesh_3/CGAL/IO/File_medit.h
@@ -3,7 +3,7 @@ namespace CGAL {
 /// \ingroup PkgMesh_3IOFunctions
 ///
 /// \brief Outputs a mesh complex to the medit (`.mesh`) file format.
-///        See \cgalCite{frey:inria-00069921} for a detailed presentation of this file format.
+///        See \cgalCite{frey:inria-00069921} for a comprehensive description of this file format.
 ///
 /// \param os the output stream
 /// \param c3t3 the mesh complex
diff --git a/Mesh_3/include/CGAL/IO/File_medit.h b/Mesh_3/include/CGAL/IO/File_medit.h
index a0c25b33124..8b12c81e1c4 100644
--- a/Mesh_3/include/CGAL/IO/File_medit.h
+++ b/Mesh_3/include/CGAL/IO/File_medit.h
@@ -879,10 +879,7 @@ void
 output_to_medit(std::ostream& os,
                 const C3T3& c3t3,
                 bool rebind = false,
-                bool show_patches = false,
-                typename boost::enable_if_c<
-                           boost::is_same<typename C3T3::Triangulation::Periodic_tag,
-                                          Tag_false>::value>::type* = NULL)
+                bool show_patches = false)
 {
   if ( rebind )
   {
diff --git a/Mesh_3/include/CGAL/Mesh_3/Dump_c3t3.h b/Mesh_3/include/CGAL/Mesh_3/Dump_c3t3.h
index 2df445be16f..7dd4bcf73c7 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Dump_c3t3.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Dump_c3t3.h
@@ -25,12 +25,15 @@
 #include <CGAL/license/Mesh_3.h>
 
 #include <CGAL/disable_warnings.h>
-#include <string>
+
 #include <CGAL/Mesh_3/io_signature.h>
 #include <CGAL/Mesh_3/Mesh_complex_3_in_triangulation_3_base.h>
+#include <CGAL/IO/File_medit.h>
+
 #include <CGAL/is_streamable.h>
-#include <boost/type_traits/is_same.hpp>
+
 #include <fstream>
+#include <string>
 
 namespace CGAL {
 
@@ -50,14 +53,9 @@ struct Dump_c3t3 {
   {
     std::clog<<"======dump c3t3===== to: " << prefix << std::endl;
     std::ofstream medit_file((prefix+".mesh").c_str());
-
-    // This medit function is meant to be used with Mesh_3 only
-    if(boost::is_same<typename C3t3::Triangulation::Periodic_tag, Tag_false>::value)
-    {
-      medit_file.precision(17);
-      CGAL::output_to_medit(medit_file, c3t3, false, true);
-      medit_file.close();
-    }
+    medit_file.precision(17);
+    CGAL::output_to_medit(medit_file, c3t3, false /*rebind*/, true /*show_patches*/);
+    medit_file.close();
 
     std::string bin_filename = prefix;
     bin_filename += ".binary.cgal";
diff --git a/Periodic_3_mesh_3/doc/Periodic_3_mesh_3/CGAL/Periodic_3_mesh_3/IO/File_medit.h b/Periodic_3_mesh_3/doc/Periodic_3_mesh_3/CGAL/Periodic_3_mesh_3/IO/File_medit.h
index 9d64d012cee..dcd2c767721 100644
--- a/Periodic_3_mesh_3/doc/Periodic_3_mesh_3/CGAL/Periodic_3_mesh_3/IO/File_medit.h
+++ b/Periodic_3_mesh_3/doc/Periodic_3_mesh_3/CGAL/Periodic_3_mesh_3/IO/File_medit.h
@@ -3,7 +3,7 @@ namespace CGAL {
 /// \ingroup PkgPeriodic_3_mesh_3IOFunctions
 ///
 /// \brief Outputs a periodic mesh to the medit (`.mesh`) file format.
-///        See \cgalCite{frey:inria-00069921} for a detailed presentation of this file format.
+///        See \cgalCite{frey:inria-00069921} for a comprehensive description of this file format.
 ///
 /// \param os the output stream
 /// \param c3t3 the mesh complex
@@ -16,11 +16,11 @@ namespace CGAL {
 ///                     using the label of each adjacent cell.
 ///
 template <class C3T3>
-void output_to_medit(std::ostream& os,
-                     const C3T3& c3t3,
-                     int occurrence_count = 8,
-                     bool distinguish_copies = true,
-                     bool rebind = false,
-                     bool show_patches = false);
+void output_periodic_mesh_to_medit(std::ostream& os,
+                                   const C3T3& c3t3,
+                                   int occurrence_count = 8,
+                                   bool distinguish_copies = true,
+                                   bool rebind = false,
+                                   bool show_patches = false);
 
 } // namespace CGAL
diff --git a/Periodic_3_mesh_3/doc/Periodic_3_mesh_3/PackageDescription.txt b/Periodic_3_mesh_3/doc/Periodic_3_mesh_3/PackageDescription.txt
index 33203b07c42..774d697a571 100644
--- a/Periodic_3_mesh_3/doc/Periodic_3_mesh_3/PackageDescription.txt
+++ b/Periodic_3_mesh_3/doc/Periodic_3_mesh_3/PackageDescription.txt
@@ -103,7 +103,7 @@ Many classes and functions used by this package are defined within the package
 and \ref PkgMesh_3Parameters.
 
 ## Input/Output Functions ##
-- \link PkgPeriodic_3_mesh_3IOFunctions `CGAL::output_to_medit()` \endlink
+- \link PkgPeriodic_3_mesh_3IOFunctions `CGAL::output_periodic_mesh_to_medit()` \endlink
 
 
 */
diff --git a/Periodic_3_mesh_3/doc/Periodic_3_mesh_3/Periodic_3_mesh_3.txt b/Periodic_3_mesh_3/doc/Periodic_3_mesh_3/Periodic_3_mesh_3.txt
index 6cd8d260997..6a5699fd65f 100644
--- a/Periodic_3_mesh_3/doc/Periodic_3_mesh_3/Periodic_3_mesh_3.txt
+++ b/Periodic_3_mesh_3/doc/Periodic_3_mesh_3/Periodic_3_mesh_3.txt
@@ -459,7 +459,7 @@ This section presents various use cases of the periodic mesh generator.
 \subsection Periodic_3_mesh_3SubMultipleCopies Outputting Multiple Copies of a Periodic Mesh
 
 Generated meshes can be output to the `.mesh` file format, which can be read
-with `medit`. The function \link PkgPeriodic_3_mesh_3IOFunctions `CGAL::output_to_medit()` \endlink
+with `medit`. The function \link PkgPeriodic_3_mesh_3IOFunctions `CGAL::output_periodic_mesh_to_medit()` \endlink
 takes a stream, a mesh complex, and - optionally - the number of periodic copies that should be drawn,
 making it easier to observe the periodicity of the result.
 \cgalFigureRef{Periodic_3_mesh_3Periodic_copies} illustrates the different output
diff --git a/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_multi_domain.cpp b/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_multi_domain.cpp
index 1b4b26552dd..a1308ea3c39 100644
--- a/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_multi_domain.cpp
+++ b/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_multi_domain.cpp
@@ -89,9 +89,9 @@ int main(int argc, char** argv)
 
   // Output
   std::ofstream medit_file("output_multi_domain.mesh");
-  CGAL::output_to_medit<C3t3>(medit_file, c3t3, number_of_copies_in_output,
-                              false /*do not associate different colors to each copy*/,
-                              false /*do not rebind*/, true /*show patches*/);
+  CGAL::output_periodic_mesh_to_medit<C3t3>(medit_file, c3t3, number_of_copies_in_output,
+                                            false /*do not associate different colors to each copy*/,
+                                            false /*do not rebind*/, true /*show patches*/);
 
   std::cout << "EXIT SUCCESS" << std::endl;
   return 0;
diff --git a/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape.cpp b/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape.cpp
index 0211eed42e9..7d0f7fe45a3 100644
--- a/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape.cpp
+++ b/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape.cpp
@@ -68,7 +68,7 @@ int main(int argc, char** argv)
   C3t3 c3t3 = CGAL::make_periodic_3_mesh_3<C3t3>(domain, criteria);
 
   std::ofstream medit_file("output_implicit_shape.mesh");
-  CGAL::output_to_medit(medit_file, c3t3, number_of_copies_in_output);
+  CGAL::output_periodic_mesh_to_medit(medit_file, c3t3, number_of_copies_in_output);
 
   std::cout << "EXIT SUCCESS" << std::endl;
   return 0;
diff --git a/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape_with_features.cpp b/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape_with_features.cpp
index fd048a34d5e..f83cd643645 100644
--- a/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape_with_features.cpp
+++ b/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape_with_features.cpp
@@ -110,13 +110,13 @@ int main(int argc, char** argv)
   C3t3 c3t3 = CGAL::make_periodic_3_mesh_3<C3t3>(domain, criteria, no_features(),
                                                  no_exude(), no_perturb());
   std::ofstream medit_file("output_implicit_shape_without_protection.mesh");
-  CGAL::output_to_medit(medit_file, c3t3, number_of_copies_in_output);
+  CGAL::output_periodic_mesh_to_medit(medit_file, c3t3, number_of_copies_in_output);
 
   // Mesh generation WITH feature preservation (and no optimizers)
   C3t3 c3t3_bis = CGAL::make_periodic_3_mesh_3<C3t3>(domain, criteria, features(),
                                                      no_exude(), no_perturb());
   std::ofstream medit_file_bis("output_implicit_shape_with_protection.mesh");
-  CGAL::output_to_medit(medit_file_bis, c3t3_bis, number_of_copies_in_output);
+  CGAL::output_periodic_mesh_to_medit(medit_file_bis, c3t3_bis, number_of_copies_in_output);
 
   std::cout << "EXIT SUCCESS" << std::endl;
   return 0;
diff --git a/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape_with_optimizers.cpp b/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape_with_optimizers.cpp
index 80d73d13f70..1bf84816848 100644
--- a/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape_with_optimizers.cpp
+++ b/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape_with_optimizers.cpp
@@ -76,7 +76,7 @@ int main(int argc, char** argv)
                                                  exude(sliver_bound=10, time_limit=0));
 
   std::ofstream medit_file("output_implicit_shape_optimized.mesh");
-  CGAL::output_to_medit(medit_file, c3t3);
+  CGAL::output_periodic_mesh_to_medit(medit_file, c3t3);
 
   // Below, the mesh generation and the optimizations are done in several calls
   C3t3 c3t3_bis = CGAL::make_periodic_3_mesh_3<C3t3>(domain, criteria,
@@ -84,7 +84,7 @@ int main(int argc, char** argv)
                                                      no_perturb(), no_exude());
 
   std::ofstream medit_file_bis("output_implicit_shape_non-optimized.mesh");
-  CGAL::output_to_medit(medit_file_bis, c3t3_bis);
+  CGAL::output_periodic_mesh_to_medit(medit_file_bis, c3t3_bis);
 
   // Now, call each optimizer with its global function
   CGAL::odt_optimize_periodic_3_mesh_3(c3t3_bis, domain, convergence=0.03, freeze_bound=0.02, time_limit=30);
@@ -93,7 +93,7 @@ int main(int argc, char** argv)
   CGAL::exude_periodic_3_mesh_3(c3t3_bis, sliver_bound=10, time_limit=0);
 
   std::ofstream medit_file_ter("output_implicit_shape_two_steps.mesh");
-  CGAL::output_to_medit(medit_file_ter, c3t3_bis, number_of_copies_in_output);
+  CGAL::output_periodic_mesh_to_medit(medit_file_ter, c3t3_bis, number_of_copies_in_output);
 
   std::cout << "EXIT SUCCESS" << std::endl;
   return 0;
diff --git a/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape_with_subdomains.cpp b/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape_with_subdomains.cpp
index 5ab0c9b8d18..4d6c01aff53 100644
--- a/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape_with_subdomains.cpp
+++ b/Periodic_3_mesh_3/examples/Periodic_3_mesh_3/mesh_implicit_shape_with_subdomains.cpp
@@ -78,7 +78,7 @@ int main(int argc, char** argv)
 
   // Output
   std::ofstream medit_file("output_implicit_with_subdomains.mesh");
-  CGAL::output_to_medit(medit_file, c3t3, number_of_copies_in_output);
+  CGAL::output_periodic_mesh_to_medit(medit_file, c3t3, number_of_copies_in_output);
 
   std::cout << "EXIT SUCCESS" << std::endl;
   return 0;
diff --git a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/IO/File_medit.h b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/IO/File_medit.h
index 41074221d75..3aa92626c88 100644
--- a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/IO/File_medit.h
+++ b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/IO/File_medit.h
@@ -353,15 +353,12 @@ void output_to_medit(std::ostream& os,
  *                     each adjacent cell.
  */
 template <class C3T3>
-void output_to_medit(std::ostream& os,
-                     const C3T3& c3t3,
-                     const int occurrence_count = 8,
-                     const bool distinguish_copies = true,
-                     bool rebind = false,
-                     bool show_patches = false,
-                     typename boost::enable_if_c<
-                                boost::is_same<typename C3T3::Triangulation::Periodic_tag,
-                                               Tag_true>::value>::type* = NULL)
+void output_periodic_mesh_to_medit(std::ostream& os,
+                                   const C3T3& c3t3,
+                                   const int occurrence_count = 8,
+                                   const bool distinguish_copies = true,
+                                   bool rebind = false,
+                                   bool show_patches = false)
 {
   if(rebind)
   {
diff --git a/Periodic_3_mesh_3/test/Periodic_3_mesh_3/test_implicit_shapes_bunch.cpp b/Periodic_3_mesh_3/test/Periodic_3_mesh_3/test_implicit_shapes_bunch.cpp
index 5cfc2462f53..e281ebee9fb 100644
--- a/Periodic_3_mesh_3/test/Periodic_3_mesh_3/test_implicit_shapes_bunch.cpp
+++ b/Periodic_3_mesh_3/test/Periodic_3_mesh_3/test_implicit_shapes_bunch.cpp
@@ -244,7 +244,7 @@ int main()
 
     // Output
     std::ofstream medit_file(file_name.c_str());
-    CGAL::output_to_medit(medit_file, c3t3);
+    CGAL::output_periodic_mesh_to_medit(medit_file, c3t3);
   }
 
   std::cout << "EXIT SUCCESS" << std::endl;
diff --git a/Periodic_3_mesh_3/test/Periodic_3_mesh_3/test_implicit_shapes_with_features.cpp b/Periodic_3_mesh_3/test/Periodic_3_mesh_3/test_implicit_shapes_with_features.cpp
index 25f753bb206..5edf07d7005 100644
--- a/Periodic_3_mesh_3/test/Periodic_3_mesh_3/test_implicit_shapes_with_features.cpp
+++ b/Periodic_3_mesh_3/test/Periodic_3_mesh_3/test_implicit_shapes_with_features.cpp
@@ -2,8 +2,8 @@
 
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 
-#include <CGAL/Periodic_3_mesh_3/IO/File_medit.h>
 #include <CGAL/make_periodic_3_mesh_3.h>
+#include <CGAL/Periodic_3_mesh_3/IO/File_medit.h>
 #include <CGAL/Periodic_3_mesh_triangulation_3.h>
 #include <CGAL/Periodic_3_wrapper.h>
 
@@ -97,7 +97,7 @@ void test_protected_sphere()
 
   // Output
   std::ofstream medit_file_bis("protected_sphere.mesh");
-  CGAL::output_to_medit(medit_file_bis, c3t3_bis);
+  CGAL::output_periodic_mesh_to_medit(medit_file_bis, c3t3_bis);
 }
 
 ////////////////////////////////////////////////////////////////////////////////
@@ -162,7 +162,7 @@ void test_protected_squary_cylinder()
 
   // Output
   std::ofstream medit_file_bis("squary_cylinder.mesh");
-  CGAL::output_to_medit(medit_file_bis, c3t3_bis);
+  CGAL::output_periodic_mesh_to_medit(medit_file_bis, c3t3_bis);
 }
 ////////////////////////////////////////////////////////////////////////////////
 
@@ -275,7 +275,7 @@ void test_protected_squary_cylinder_2()
 
   // Output
   std::ofstream medit_file_bis("squary_cylinder_2.mesh");
-  CGAL::output_to_medit(medit_file_bis, c3t3_bis);
+  CGAL::output_periodic_mesh_to_medit(medit_file_bis, c3t3_bis);
 }
 ////////////////////////////////////////////////////////////////////////////////
 
diff --git a/Periodic_3_mesh_3/test/Periodic_3_mesh_3/test_triply_periodic_minimal_surfaces.cpp b/Periodic_3_mesh_3/test/Periodic_3_mesh_3/test_triply_periodic_minimal_surfaces.cpp
index 64fbb6a2703..0034cbd793e 100644
--- a/Periodic_3_mesh_3/test/Periodic_3_mesh_3/test_triply_periodic_minimal_surfaces.cpp
+++ b/Periodic_3_mesh_3/test/Periodic_3_mesh_3/test_triply_periodic_minimal_surfaces.cpp
@@ -305,7 +305,7 @@ int main(int, char**)
         oss_2 << iter->first << "__" << it->first << "__" << *i  << ".mesh";
         std::string output_filename = oss_2.str();
         std::ofstream medit_file( output_filename.data() );
-        CGAL::output_to_medit(medit_file, c3t3, *i);
+        CGAL::output_periodic_mesh_to_medit(medit_file, c3t3, *i);
         medit_file.close();
 
         std::cout << ", " << *i << "-copy Saved" << std::flush;