diff --git a/STL_Extension/include/CGAL/Compact_container.h b/STL_Extension/include/CGAL/Compact_container.h
index 8e665e83c1e..ad10438d026 100644
--- a/STL_Extension/include/CGAL/Compact_container.h
+++ b/STL_Extension/include/CGAL/Compact_container.h
@@ -1166,19 +1166,32 @@ public:
   }
 };
 
-struct With_point_tag {};
+struct With_point_tag {
+  int offset = 0;
+};
 
 template <class DSC, bool Const>
 struct Output_rep<CGAL::internal::CC_iterator<DSC, Const>, With_point_tag>
   : public Output_rep<CGAL::internal::CC_iterator<DSC, Const>>
 {
-  using Base = Output_rep<CGAL::internal::CC_iterator<DSC, Const>>;
+  int offset = 0;
+
+  using CC_iterator = CGAL::internal::CC_iterator<DSC, Const>;
+  using Compact_container = typename CC_iterator::CC;
+  using Time_stamper = typename Compact_container::Time_stamper;
+  using Base = Output_rep<CC_iterator>;
   using Base::Base;
 
+  Output_rep(const CC_iterator it, With_point_tag tag = {})
+    : Base(it), offset(tag.offset) {}
+
   std::ostream& operator()(std::ostream& out) const {
-    Base::operator()(out);
-    if(this->it.operator->() != nullptr)
-      return  out << "= " << this->it->point();
+    out << Time_stamper::display_id(this->it.operator->(), offset);
+    if(this->it.operator->() != nullptr) {
+      if(Time_stamper::time_stamp(this->it.operator->()) == 0)
+        return out << "= infinite_vertex()";
+      return out << "= " << this->it->point();
+    }
     else
       return out;
   }
diff --git a/STL_Extension/include/CGAL/Time_stamper.h b/STL_Extension/include/CGAL/Time_stamper.h
index 0fcee819220..a1f2d30eb36 100644
--- a/STL_Extension/include/CGAL/Time_stamper.h
+++ b/STL_Extension/include/CGAL/Time_stamper.h
@@ -67,12 +67,12 @@ struct Time_stamper
     return pt->time_stamp();
   }
 
-  static auto display_id(const T* pt)
+  static auto display_id(const T* pt, int offset = 0)
   {
     if(pt == nullptr)
       return std::string("nullptr");
     else
-      return std::string("#") + std::to_string(pt->time_stamp());
+      return std::string("#") + std::to_string(pt->time_stamp() + offset);
   }
 
   static std::size_t hash_value(const T* p) {
@@ -110,7 +110,7 @@ public:
     return 0;
   }
 
-  static auto display_id(const T* pt)
+  static auto display_id(const T* pt, int)
   {
     return static_cast<const void*>(pt);
   }
diff --git a/Stream_support/include/CGAL/IO/io.h b/Stream_support/include/CGAL/IO/io.h
index 1cbb8054ba8..71308a423c6 100644
--- a/Stream_support/include/CGAL/IO/io.h
+++ b/Stream_support/include/CGAL/IO/io.h
@@ -183,7 +183,7 @@ class Output_rep
 
 public:
   //! initialize with a const reference to \a t.
-  Output_rep( const T& tt) : t(tt) {}
+  Output_rep( const T& tt, F = {}) : t(tt) {}
   //! perform the output, calls \c operator\<\< by default.
   std::ostream& operator()( std::ostream& os) const { return (os << t); }
 };
@@ -248,7 +248,7 @@ Convenience function to construct an output representation (`Output_rep`) for ty
 Generic IO for type `T` with formatting tag.
 */
 template <class T, class F>
-Output_rep<T,F> oformat( const T& t, F) { return Output_rep<T,F>(t); }
+Output_rep<T,F> oformat( const T& t, F format) { return Output_rep<T,F>(t, format); }
 
 } // namespace IO
 
diff --git a/TDS_3/include/CGAL/Triangulation_simplex_3.h b/TDS_3/include/CGAL/Triangulation_simplex_3.h
index 0754fb021c5..91db819c098 100644
--- a/TDS_3/include/CGAL/Triangulation_simplex_3.h
+++ b/TDS_3/include/CGAL/Triangulation_simplex_3.h
@@ -280,6 +280,57 @@ operator<< (std::ostream& os,
   return os;
 }
 
+template < typename TriangulationDataStructure_3, typename Tag >
+struct Output_rep<Triangulation_simplex_3<TriangulationDataStructure_3>, Tag >
+{
+  using TDS = TriangulationDataStructure_3;
+  using Simplex = Triangulation_simplex_3<TriangulationDataStructure_3>;
+  using Vertex_handle = typename Simplex::Vertex_handle;
+  using Edge = typename Simplex::Edge;
+  using Facet = typename Simplex::Facet;
+  using Cell_handle = typename Simplex::Cell_handle;
+
+  Simplex simplex;
+  Tag tag;
+
+  std::ostream& operator()(std::ostream& os) const {
+    auto display_vert = [&](auto v) {
+      return CGAL::IO::oformat(v, tag);
+    };
+    switch(simplex.dimension()) {
+      case 0: {
+        os << "vertex " << display_vert(static_cast<Vertex_handle>(simplex));
+        break;
+      }
+      case 1: {
+        const auto [c, index1, index2] = static_cast<Edge>(simplex);
+        os << "edge "
+           << display_vert(c->vertex(index1)) << " - "
+           << display_vert(c->vertex(index2));
+        break;
+      }
+      case 2: {
+        const auto [c, index] = static_cast<Facet>(simplex);
+        os << "facet "
+           << display_vert(c->vertex(TDS::vertex_triple_index(index, 0))) << " - "
+           << display_vert(c->vertex(TDS::vertex_triple_index(index, 1))) << " - "
+           << display_vert(c->vertex(TDS::vertex_triple_index(index, 2)));
+        break;
+      }
+      case 3: {
+        const auto c = static_cast<Cell_handle>(simplex);
+        os << "cell "
+           << display_vert(c->vertex(0)) << " - "
+           << display_vert(c->vertex(1)) << " - "
+           << display_vert(c->vertex(2)) << " - "
+           << display_vert(c->vertex(3));
+        break;
+      }
+      default: CGAL_assume(false);
+    }
+    return os;
+  }
+};
 
 } //namespace CGAL