diff --git a/Combinatorial_map/include/CGAL/Combinatorial_map_storages_with_index.h b/Combinatorial_map/include/CGAL/Combinatorial_map_storages_with_index.h
index 584442412c54..139c93c720f8 100644
--- a/Combinatorial_map/include/CGAL/Combinatorial_map_storages_with_index.h
+++ b/Combinatorial_map/include/CGAL/Combinatorial_map_storages_with_index.h
@@ -75,7 +75,7 @@ namespace CGAL {
     struct Container_for_attributes : public
         Compact_container_with_index<T,
         typename Allocator_traits::template rebind_alloc<T>,
-        Multiply_by_two_policy_for_cc_with_size<64>, size_type >
+        Multiply_by_two_policy_for_cc_with_size<64>, Index_type >
     {};
     /// Typedef for attributes
     typedef typename internal::template Get_attributes_tuple<Dart_wrapper>::type
diff --git a/Generalized_map/include/CGAL/Generalized_map_storages_with_index.h b/Generalized_map/include/CGAL/Generalized_map_storages_with_index.h
index 828004b84164..ebb88cb0b3fd 100644
--- a/Generalized_map/include/CGAL/Generalized_map_storages_with_index.h
+++ b/Generalized_map/include/CGAL/Generalized_map_storages_with_index.h
@@ -75,7 +75,7 @@ namespace CGAL {
     struct Container_for_attributes : public
         Compact_container_with_index<T,
         typename Allocator_traits::template rebind_alloc<T>,
-        Multiply_by_two_policy_for_cc_with_size<64>, size_type >
+        Multiply_by_two_policy_for_cc_with_size<64>, Index_type >
     {};
     /// Typedef for attributes
     typedef typename internal::template Get_attributes_tuple<Dart_wrapper>::type
diff --git a/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h b/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h
index 8417e20b2265..be93b3726f99 100644
--- a/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h
+++ b/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h
@@ -85,7 +85,7 @@ namespace CGAL {
     struct Container_for_attributes : public
         Compact_container_with_index<T,
         typename Allocator_traits::template rebind_alloc<T>,
-        Multiply_by_two_policy_for_cc_with_size<64>, size_type >
+        Multiply_by_two_policy_for_cc_with_size<64>, Index_type >
     {};
     /// Typedef for attributes
     typedef typename internal::template Get_attributes_tuple<Dart_wrapper>::type
diff --git a/Linear_cell_complex/include/CGAL/GMap_linear_cell_complex_storages_with_index.h b/Linear_cell_complex/include/CGAL/GMap_linear_cell_complex_storages_with_index.h
index 27d58a7651af..7b17d0c389f6 100644
--- a/Linear_cell_complex/include/CGAL/GMap_linear_cell_complex_storages_with_index.h
+++ b/Linear_cell_complex/include/CGAL/GMap_linear_cell_complex_storages_with_index.h
@@ -85,7 +85,7 @@ namespace CGAL {
     struct Container_for_attributes : public
         Compact_container_with_index<T,
         typename Allocator_traits::template rebind_alloc<T>,
-        Multiply_by_two_policy_for_cc_with_size<64>, size_type >
+        Multiply_by_two_policy_for_cc_with_size<64>, Index_type >
     {};
     /// Typedef for attributes
     typedef typename internal::template Get_attributes_tuple<Dart_wrapper>::type