diff --git a/Triangulation_on_sphere_2/benchmark/CMakeLists.txt b/Triangulation_on_sphere_2/benchmark/CMakeLists.txt
index 0c97293dcc4..24bd9b0dc91 100644
--- a/Triangulation_on_sphere_2/benchmark/CMakeLists.txt
+++ b/Triangulation_on_sphere_2/benchmark/CMakeLists.txt
@@ -1,34 +1,20 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
+project( Triangulation_on_sphere_2_Benchmarks )
 
-project( Implantation_example )
+cmake_minimum_required(VERSION 3.1...3.15)
 
-CMAKE_MINIMUM_REQUIRED(VERSION 2.4.5)
-
-set(CMAKE_ALLOW_LOOSE_LOOP_CONSTRUCTS true)
- 
-if ( COMMAND cmake_policy )
-  cmake_policy( SET CMP0003 NEW )  
-endif()
- 
-find_package(CGAL QUIET COMPONENTS Core )
+find_package(CGAL REQUIRED COMPONENTS Core )
 
 if ( CGAL_FOUND )
 
-  include( ${CGAL_USE_FILE} )
-
-  include( CGAL_CreateSingleSourceCGALProgram )
-
-  include_directories (../include)
-
-  create_single_source_cgal_program( "bench_regular_triangulation_on_sphere.cpp" )
+  create_single_source_cgal_program( "bench_dtos2.cpp" )
   create_single_source_cgal_program( "generate_points.cpp" )
- 
 
 else()
-  
+
     message(STATUS "This program requires the CGAL library, and will not be compiled.")
-  
+
 endif()
 
diff --git a/Triangulation_on_sphere_2/benchmark/random_dtos2.cpp b/Triangulation_on_sphere_2/benchmark/bench_dtos2.cpp
similarity index 73%
rename from Triangulation_on_sphere_2/benchmark/random_dtos2.cpp
rename to Triangulation_on_sphere_2/benchmark/bench_dtos2.cpp
index 3ec4683e56d..0385b41db3f 100644
--- a/Triangulation_on_sphere_2/benchmark/random_dtos2.cpp
+++ b/Triangulation_on_sphere_2/benchmark/bench_dtos2.cpp
@@ -1,7 +1,4 @@
-// @fixme should be in benchmarks really
-
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
-#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
 
 #include <CGAL/Delaunay_triangulation_on_sphere_traits_2.h>
 #include <CGAL/Delaunay_triangulation_on_sphere_2.h>
@@ -12,7 +9,7 @@
 #include <CGAL/Delaunay_triangulation_3.h>
 #include <CGAL/point_generators_2.h>
 #include <CGAL/point_generators_3.h>
-#include <CGAL/Polyhedron_3.h>
+#include <CGAL/Surface_mesh.h>
 #include <CGAL/squared_distance_3.h>
 #include <CGAL/Timer.h>
 
@@ -23,7 +20,7 @@
 #include <vector>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel    K;
-typedef CGAL::Polyhedron_3<K>                                  Polyhedron_3;
+typedef CGAL::Surface_mesh<K>                                  Surface_mesh;
 
 typedef K::Segment_3                                           Segment_3;
 typedef CGAL::Delaunay_triangulation_3<K>                      Delaunay;
@@ -44,8 +41,10 @@ int main(int, char**)
   const std::size_t nu_of_pts = 1e7;
   const double radius = 5184.152;
 
-  CGAL::Random random(nu_of_pts);
-  CGAL::Random_points_on_sphere_3<Point, Creator> on_sphere(radius);
+  CGAL::Random random;
+  std::cout << "Seed is " << random.get_seed() << std::endl;
+
+  CGAL::Random_points_on_sphere_3<Point, Creator> on_sphere(radius, random);
 
   std::vector<Point> points;
   points.reserve(nu_of_pts);
@@ -63,7 +62,8 @@ int main(int, char**)
   dtos.insert(points.begin(), points.end());
   time.stop();
   assert(dtos.number_of_vertices() == nu_of_pts);
-  std::cout << "Triangulation sphere: " << time.time() << std::endl;
+  std::cout << "Triangulation sphere: "
+            << dtos.number_of_vertices() << " vertices in " << time.time() << " sec" << std::endl;
 
   //Triangulation with points on the sphere (projection_traits)
   Gt2 traits(K::Point_3(0, 0, 0), radius);
@@ -75,15 +75,16 @@ int main(int, char**)
   dtos2.insert(boost::make_transform_iterator(points.begin(), cst),
                boost::make_transform_iterator(points.end(), cst));
   time.stop();
-  std::cout << "Triangulation sphere projection traits: "<< time.time() << std::endl;
+  std::cout << "Triangulation w/ sphere projection traits: "
+            << dtos2.number_of_vertices() << " vertices in " << time.time() << " sec" << std::endl;
 
-  Polyhedron_3 poly;
+//  Surface_mesh sm;
 
-  time.reset();
-  time.start();
-  CGAL::convex_hull_3(points.begin(), points.end(), poly);
-  time.stop();
-  std::cout << "Convex hull: " << time.time() << " " << std::endl;
+//  time.reset();
+//  time.start();
+//  CGAL::convex_hull_3(points.begin(), points.end(), sm);
+//  time.stop();
+//  std::cout << "Convex hull 3D: " << time.time() << " " << std::endl;
 
   time.reset();
   time.start();
@@ -91,7 +92,8 @@ int main(int, char**)
   T.insert(Point(0, 0, 0));
   T.insert(points.begin(), points.end());
   time.stop();
-  std::cout << "Delaunay on sphere: " << time.time() << std::endl;
+  std::cout << "Delaunay 3D with origin: "
+            << T.number_of_vertices() << " vertices in " << time.time() << " sec" << std::endl;
 
   time.reset();
   time.start();
@@ -99,7 +101,7 @@ int main(int, char**)
   T_fast_on2.insert(Point(0, 0, 0));
   T_fast_on2.insert(points.begin(), points.end());
   time.stop();
-  std::cout << "Delaunay fast location on sphere: " << time.time() << std::endl;
+  std::cout << "Delaunay 3D with origin, fast location: " << time.time() << std::endl;
 
   return EXIT_SUCCESS;
 }
diff --git a/Triangulation_on_sphere_2/benchmark/bench_regular_triangulation_on_sphere.cpp b/Triangulation_on_sphere_2/benchmark/bench_regular_triangulation_on_sphere.cpp
deleted file mode 100644
index 07f6b74b08c..00000000000
--- a/Triangulation_on_sphere_2/benchmark/bench_regular_triangulation_on_sphere.cpp
+++ /dev/null
@@ -1,88 +0,0 @@
-//#define CGAL_NO_STATIC_FILTERS
-
-#include <CGAL/basic.h>
-
-#include <CGAL/Cartesian.h>
-#include <CGAL/MP_Float.h>
-#include <CGAL/Quotient.h>
-#include <CGAL/Gmpq.h>
-
-//robust classes
-#include <CGAL/Regular_triangulation_sphere_traits_2.h>
-#include <CGAL/Regular_triangulation_on_sphere_2.h>
-//#include <CGAL/Triangulation_sphere_traits_2.h>
-#include <CGAL/Triangulation_on_sphere_2.h>
-
-//manuel prototypes
-//#include <CGAL/Regular_triangulation_sphere_traits_2_manuel_proto.h>
-//#include <CGAL/Regular_triangulation_on_sphere_2_manuel_proto.h>
-//#include <CGAL/Triangulation_on_sphere_2_manuel_proto.h>
-
-#include <CGAL/Random.h>
-#include <CGAL/Timer.h>
-#include <CGAL/point_generators_3.h>
-#include <CGAL/point_generators_2.h>
-#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
-
-typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
-
-typedef CGAL::Regular_triangulation_sphere_traits_2< K > FK;
-template class CGAL::Regular_triangulation_on_sphere_2<FK>;
-typedef CGAL::Regular_triangulation_on_sphere_2<FK>  RTOS;
-
-//typedef CGAL::Regular_triangulation_sphere_traits_2_manuel_proto< K > FK2;
-//template class CGAL::Regular_triangulation_on_sphere_2_manuel_proto<FK2>;
-//typedef CGAL::Regular_triangulation_on_sphere_2_manuel_proto<FK2> RTOSPROTO;
-
-void compute_times()
-{
-  int no_of_pts;
-
-  typedef K::Point_3 Point_3;
-  std::list<Point_3> pts3;
-
-  // std::cin >> no_of_pts;
-  no_of_pts = 1000;
-  for(int count=0; count<no_of_pts; ++count)
-  {
-    Point_3 p;
-    std::cin >> p;
-    if(p != Point_3(0,0,0)) pts3.push_back(p);
-    else count--;
-  }
-
-  std::cout << "REGULAR TRIANGULATION ON SPHERE" << std::endl;
-  {
-    RTOS rtos;
-    //rtos.insert_four_init_vertices();
-    {
-      CGAL::Timer timer_reg; timer_reg.start();
-      rtos.insert(pts3.begin(),pts3.end());
-      timer_reg.stop();
-      std::cout << timer_reg.time() << std::endl;
-    }
-
-    if(!rtos.is_valid())
-      std::cout << "problem!" << std::endl;
-  }
-
-  std::cout << "REGULAR TRIANGULATION ON SPHERE PROTO" << std::endl;
-  {
-    RTOS rtosprot;
-    {
-      CGAL::Timer timer_reg; timer_reg.start();
-      rtosprot.insert(pts3.begin(),pts3.end());
-      timer_reg.stop();
-      std::cout << timer_reg.time() << std::endl;
-    }
-    if(!rtosprot.is_valid()) { std::cout << "problem!" << std::endl; exit(0); }
-  }
-}
-
-int main(int /*argc*/, char** /*argv*/)
-{
-  compute_times();
-
-  return EXIT_SUCCESS;
-}
-
diff --git a/Triangulation_on_sphere_2/benchmark/generate_points.cpp b/Triangulation_on_sphere_2/benchmark/generate_points.cpp
index 560b27d9f21..152145abf16 100644
--- a/Triangulation_on_sphere_2/benchmark/generate_points.cpp
+++ b/Triangulation_on_sphere_2/benchmark/generate_points.cpp
@@ -1,36 +1,38 @@
-#include <CGAL/basic.h>
-
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
 #include <CGAL/Random.h>
 #include <CGAL/point_generators_3.h>
 
-
 typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
 
+int main(int argc, char* argv[])
+{
+  int no_of_pts;
+  double radius;
+  if(argc > 1)
+  {
+    no_of_pts = pow(10, atoi(argv[1]));
+    radius = atoi(argv[2]);
+  }
+  else
+  {
+    no_of_pts = 1000000;
+    radius = 1;
+  }
 
-int main(int argc, char* argv[]) {
- int no_of_pts;
- double radius;
- if (argc > 1) {
-   no_of_pts = pow(10,atoi(argv[1]));
-   radius = atoi(argv[2]);
- } else {
-   no_of_pts = 1000000;
-   radius=1;
- }
+  CGAL::Random random(7);
+  typedef CGAL::Creator_uniform_3<double, K::Point_3> Creator;
 
+  std::cout << no_of_pts << std::endl;
 
- CGAL::Random random(7);
- typedef CGAL::Creator_uniform_3<double, K::Point_3> Creator;
+  CGAL::Random_points_on_sphere_3<K::Point_3, Creator> on_sphere(radius, random);
+  for(int count=0; count<no_of_pts; ++count)
+  {
+    K::Point_3 p = *on_sphere;
+    ++on_sphere;
 
- std::cout << no_of_pts << std::endl;  
+    std::cout << p << std::endl;
+  }
 
- CGAL::Random_points_on_sphere_3<K::Point_3, Creator> on_sphere(radius, random);
- for (int count=0; count<no_of_pts; count++) {
-   K::Point_3 p = *on_sphere; on_sphere ++;
-   std::cout << p << std::endl;
- }
-
-
- return 0;
+  return EXIT_SUCCESS;
 }