diff --git a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h
index 6c9c319c71e..4d552c52af7 100644
--- a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h
+++ b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h
@@ -1705,6 +1705,11 @@ public:
     return _tds.cells_end();
   }
 
+  auto finite_cell_handles() const
+  {
+    return _tds.cell_handles();
+  }
+
   Vertex_iterator finite_vertices_begin() const {
     return _tds.vertices_begin();
   }
@@ -1712,6 +1717,11 @@ public:
     return _tds.vertices_end();
   }
 
+  auto finite_vertex_handles() const
+  {
+    return _tds.vertex_handles();
+  }
+
   Edge_iterator finite_edges_begin() const {
     return _tds.edges_begin();
   }
@@ -1909,6 +1919,29 @@ public:
     return _tds.mirror_facet(f);
   }
 
+  /// Vertex ranges defining a simplex
+  static std::array<Vertex_handle, 2> vertices(const Edge& e)
+  {
+    return std::array<Vertex_handle, 2>{
+             e.first->vertex(e.second),
+             e.first->vertex(e.third)};
+  }
+  static std::array<Vertex_handle, 3> vertices(const Facet& f)
+  {
+    return std::array<Vertex_handle, 3>{
+             f.first->vertex(vertex_triple_index(f.second, 0)),
+             f.first->vertex(vertex_triple_index(f.second, 1)),
+             f.first->vertex(vertex_triple_index(f.second, 2))};
+  }
+  static std::array<Vertex_handle, 4> vertices(const Cell_handle c)
+  {
+    return std::array<Vertex_handle, 4>{
+             c->vertex(0),
+             c->vertex(1),
+             c->vertex(2),
+             c->vertex(3)};
+  }
+
 private:
   /** @name Checking helpers */
   /// calls has_self_edges for every cell of the triangulation