diff --git a/BGL/examples/BGL_surface_mesh/gwdwg.cpp b/BGL/examples/BGL_surface_mesh/gwdwg.cpp
index b857d5a774d..07ed87cc639 100644
--- a/BGL/examples/BGL_surface_mesh/gwdwg.cpp
+++ b/BGL/examples/BGL_surface_mesh/gwdwg.cpp
@@ -25,10 +25,10 @@ int main()
         Point_3(1,-1,-1),
         Point_3(1,1,-1),
         Point_3(-1,1,-1),
+        Point_3(-1,1,1),
         Point_3(-1,-1,1),
         Point_3(1,-1,1),
         Point_3(1,1,1),
-        Point_3(-1,1,1),
         sm
         );
 
@@ -45,10 +45,10 @@ int main()
         Point_3(0.5,-0.5,-0.5),
         Point_3(0.5,0.5,-0.5),
         Point_3(-0.5,0.5,-0.5),
+        Point_3(-0.5,0.5,0.5),
         Point_3(-0.5,-0.5,0.5),
         Point_3(0.5,-0.5,0.5),
         Point_3(0.5,0.5,0.5),
-        Point_3(-0.5,0.5,0.5),
         poly
         );
   pvertex_descriptor pvd = *  vertices(pmesh).first;
diff --git a/BGL/include/CGAL/boost/graph/helpers.h b/BGL/include/CGAL/boost/graph/helpers.h
index 7ed5fbf1447..7f2b5d3d0eb 100644
--- a/BGL/include/CGAL/boost/graph/helpers.h
+++ b/BGL/include/CGAL/boost/graph/helpers.h
@@ -868,16 +868,16 @@ make_hexahedron(const P& p0, const P& p1, const P& p2, const P& p3,
   ppmap[v6] = p6;
   ppmap[v7] = p7;
 
-  halfedge_descriptor ht = internal::make_quad(v7, v4, v5, v6, g);
-  halfedge_descriptor hb = prev(internal::make_quad(v1, v0, v3, v2, g),g);
+  halfedge_descriptor ht = internal::make_quad(v4, v5, v6, v7, g);
+  halfedge_descriptor hb = prev(internal::make_quad(v0, v3, v2, v1, g),g);
   for(int i=0; i <4; i++){
     halfedge_descriptor h = halfedge(add_edge(g),g);
     set_target(h,target(hb,g),g);
     set_next(h,opposite(hb,g),g);
-    set_next(opposite(next(ht,g),g),h,g);
+    set_next(opposite(prev(ht,g),g),h,g);
     h = opposite(h,g);
-    set_target(h,target(ht,g),g);
-    set_next(h,opposite(ht,g),g);
+    set_target(h,source(prev(ht,g),g),g);
+    set_next(h,opposite(next(next(ht,g),g),g),g);
     set_next(opposite(next(hb,g),g),h,g);
     hb = next(hb,g);
     ht = prev(ht,g);
diff --git a/BGL/test/BGL/test_helpers.cpp b/BGL/test/BGL/test_helpers.cpp
index e4d0e145829..3ba16eb4d6e 100644
--- a/BGL/test/BGL/test_helpers.cpp
+++ b/BGL/test/BGL/test_helpers.cpp
@@ -132,7 +132,7 @@ int main()
   assert(CGAL::is_triangle_mesh(m));
   assert(CGAL::is_valid_polygon_mesh(m));
   m.clear();
-  hd = CGAL::make_hexahedron(a,b,c,d,aa,bb,cc,dd,m);
+  hd = CGAL::make_hexahedron(a,b,c,d,dd,aa,bb,cc,m);
   assert(CGAL::is_hexahedron(hd,m));
   assert(CGAL::is_quad_mesh(m));
   assert(CGAL::is_valid_polygon_mesh(m));
diff --git a/Generator/test/Generator/generic_random_test.cpp b/Generator/test/Generator/generic_random_test.cpp
index 7ea066f4233..3090ddbfc80 100644
--- a/Generator/test/Generator/generic_random_test.cpp
+++ b/Generator/test/Generator/generic_random_test.cpp
@@ -288,8 +288,10 @@ int main()
   Polyhedron polyhedron;
 
   // A cube
-  make_hexahedron(Point_3(-0.5,-0.5,-0.5), Point_3(0.5,-0.5,-0.5), Point_3(0.5,0.5,-0.5), Point_3(-0.5,0.5,-0.5),
-                  Point_3(-0.5,0.5,0.5), Point_3(-0.5,-0.5,0.5), Point_3(0.5,-0.5,0.5), Point_3(0.5,0.5,0.5),
+  make_hexahedron(
+        Point_3(-0.5,-0.5,-0.5), Point_3(0.5,-0.5,-0.5), Point_3(0.5,0.5,-0.5),
+        Point_3(-0.5,0.5,-0.5), Point_3(-0.5,0.5,0.5), Point_3(-0.5,-0.5,0.5),
+        Point_3(0.5,-0.5,0.5), Point_3(0.5,0.5,0.5),
                   polyhedron);
 
   boost::graph_traits<Polyhedron>::halfedge_descriptor facets[6];