diff --git a/Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Plane_3_intersection.h b/Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Plane_3_intersection.h
index 311c397ddfa..270693f2fb9 100644
--- a/Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Plane_3_intersection.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Plane_3_intersection.h
@@ -97,6 +97,19 @@ intersection(
 
   std::vector<std::array<int,2>> neighbor_ids(14, {-1,-1});
 
+  auto add_neighbor = [&neighbor_ids](int i, int j)
+  {
+    if (neighbor_ids[i][0] == -1 ) {
+      neighbor_ids[i][0] = j;
+    }
+    else {
+      if (neighbor_ids[i][0]!=j && neighbor_ids[i][1]==-1)
+      {
+        neighbor_ids[i][1] = j;
+      }
+    }
+  };
+
   int start_id = -1;
   int solo_id = -1;
   // for each face of the bbox, we look for intersection of the plane with its edges
@@ -155,18 +168,8 @@ intersection(
       case 2:
       {
         if (start_id == -1) start_id = ids[0];
-        if (neighbor_ids[ids[0]][0] == -1) {
-          neighbor_ids[ids[0]][0] = ids[1];
-        }
-        else {
-          neighbor_ids[ids[0]][1] = ids[1];
-        }
-        if (neighbor_ids[ids[1]][0] == -1) {
-          neighbor_ids[ids[1]][0] = ids[0];
-        }
-        else {
-          neighbor_ids[ids[1]][1] = ids[0];
-        }
+        add_neighbor(ids[0], ids[1]);
+        add_neighbor(ids[1], ids[0]);
         break;
       }
       case 1:
diff --git a/Intersections_3/test/Intersections_3/test_intersections_3.cpp b/Intersections_3/test/Intersections_3/test_intersections_3.cpp
index 7247a3c472e..ea68b96e871 100644
--- a/Intersections_3/test/Intersections_3/test_intersections_3.cpp
+++ b/Intersections_3/test/Intersections_3/test_intersections_3.cpp
@@ -907,7 +907,7 @@ struct Test {
 
       //edge
       check_intersection (cub, Pl(P(1,1,1), P(1,2,1), P(1.5,0,0)),
-                          S(P(1,2,1), P(1,1,1)));
+                          S(P(1,1,1), P(1,2,1)));
 
 
       //face
@@ -924,6 +924,7 @@ struct Test {
         assert(p.x() == 1);
       }
       res = CGAL::intersection(cub, Pl(P(1,1,1), P(1,2,1), P(2,2,2)));
+
       poly = boost::get<std::vector<P> >(&*res);
       assert(poly != nullptr);
       assert(poly->size() == 4);
@@ -940,8 +941,8 @@ struct Test {
       check_intersection (cub, Pl(P(2, 1.66, 2),
                                   P(1.66,2,2),
                                   P(2,2,1.66)),
-                          Tr(P(2, 2, 1.66),
-                             P(1.66,2,2),
+                          Tr(P(1.66,2,2),
+                             P(2, 2, 1.66),
                              P(2,1.66,2)));
 
       //other edge