diff --git a/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/fast.cpp b/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/fast.cpp
index e68b0980e32..20cf6834d21 100644
--- a/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/fast.cpp
+++ b/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/fast.cpp
@@ -12,7 +12,7 @@
 
 
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
-#include <CGAL/Envelope.h>
+#include <CGAL/Polyhedral_envelope.h>
 #include <CGAL/Timer.h>
 
 #include <fstream>
@@ -28,7 +28,7 @@ int main(int argc, char* argv[])
   typedef std::array<int, 3> Vector3i;
   typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
   typedef Kernel::Point_3 Point_3;
-  typedef CGAL::Envelope<Kernel> Envelope;
+  typedef CGAL::Polyhedral_envelope<Kernel> Envelope;
 
   std::vector<Point_3> env_vertices;
   std::vector<Vector3i> env_faces;
diff --git a/Polygon_mesh_processing/include/CGAL/Polyhedral_envelope.h b/Polygon_mesh_processing/include/CGAL/Polyhedral_envelope.h
index f47df8aaa99..e9cc54c53ca 100644
--- a/Polygon_mesh_processing/include/CGAL/Polyhedral_envelope.h
+++ b/Polygon_mesh_processing/include/CGAL/Polyhedral_envelope.h
@@ -1745,13 +1745,6 @@ private:
         halfspace[i].emplace_back(plane);// number 2
 
 
-        if (obtuse != 1) {
-          plane = get_corner_plane(ver[faces[i][1]], midpoint(ver[faces[i][0]], ver[faces[i][2]]) , normal,
-                           tolerance, use_accurate_cross);
-          halfspace[i].emplace_back(plane);// number 3;
-
-        }
-
         edgedire = normalize(BC);
         // if (use_accurate_cross)edgenormaldist = accurate_cross_product_direction(ORIGIN, edgedire, ORIGIN, normal)*tolerance;
         // else
@@ -1762,12 +1755,6 @@ private:
                       ver[faces[i][1]] + edgenormaldist + normal);
         halfspace[i].emplace_back(plane);// number 4
 
-        if (obtuse != 2) {
-          plane = get_corner_plane(ver[faces[i][2]], midpoint(ver[faces[i][0]], ver[faces[i][1]]), normal,
-                           tolerance,use_accurate_cross);
-          halfspace[i].emplace_back(plane);// number 5;
-
-        }
 
         edgedire = -normalize(AC);
         // if (use_accurate_cross)edgenormaldist = accurate_cross_product_direction(ORIGIN, edgedire, ORIGIN , normal)*tolerance;
@@ -1779,11 +1766,21 @@ private:
                       ver[faces[i][0]] + edgenormaldist + normal);
         halfspace[i].emplace_back(plane);// number 6
 
+
+        if (obtuse != 1) {
+          plane = get_corner_plane(ver[faces[i][1]], midpoint(ver[faces[i][0]], ver[faces[i][2]]) , normal,
+                                   tolerance, use_accurate_cross);
+          halfspace[i].emplace_back(plane);// number 3;
+        }
         if (obtuse != 0) {
           plane = get_corner_plane(ver[faces[i][0]], midpoint(ver[faces[i][1]], ver[faces[i][2]]) , normal,
-                           tolerance,use_accurate_cross);
+                                   tolerance,use_accurate_cross);
           halfspace[i].emplace_back(plane);// number 7;
-
+        }
+        if (obtuse != 2) {
+          plane = get_corner_plane(ver[faces[i][2]], midpoint(ver[faces[i][0]], ver[faces[i][1]]), normal,
+                                   tolerance,use_accurate_cross);
+          halfspace[i].emplace_back(plane);// number 5;
         }
 
 #ifdef CGAL_ENVELOPE_DEBUG