diff --git a/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h b/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h
index 8fed0f20918..35cecade1f4 100644
--- a/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h
+++ b/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h
@@ -3476,7 +3476,6 @@ get_least_square_surface_plane(const Vertex_handle& v,
                                        tr_.geom_traits(),
                                        Default_diagonalize_traits<FT, 3>());
 
-
   // The surface center of a facet might have an offset in periodic triangulations
   const Bare_point& ref_facet_scp = ref_facet.first->get_facet_surface_center(ref_facet.second);
   const Bare_point& ref_point = tr_.get_closest_point(cp(position), ref_facet_scp);
diff --git a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_triangulation_3.h b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_triangulation_3.h
index 58b2b7d5350..0b86341b9d8 100644
--- a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_triangulation_3.h
+++ b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_triangulation_3.h
@@ -511,16 +511,19 @@ public:
     typename Geom_traits::Construct_vector_3 cv = geom_traits().construct_vector_3_object();
     typename Geom_traits::Construct_triangle_3 ct = geom_traits().construct_triangle_3_object();
 
-    CGAL_precondition(f.first->has_vertex(ref_v));
+    CGAL_precondition(f.first != Cell_handle() && f.first->has_vertex(ref_v));
     const int ref_v_pos = f.first->index(ref_v);
-    const Bare_point& ref_p = cp(point(ref_v));
-    const Bare_point& ref_p_in_f = cp(point(f.first, ref_v_pos));
+    const Bare_point ref_p = cp(point(ref_v));
+    const Bare_point ref_p_in_f = cp(point(f.first, ref_v_pos));
     Vector_3 move_to_canonical = cv(ref_p_in_f, ref_p);
 
     const int s = f.second;
-    return ct(tr(cp(point(f.first, (s+1)%4)), move_to_canonical),
-              tr(cp(point(f.first, (s+2)%4)), move_to_canonical),
-              tr(cp(point(f.first, (s+3)%4)), move_to_canonical));
+    const Bare_point mp0 = tr(cp(point(f.first, (s+1)%4)), move_to_canonical);
+    const Bare_point mp1 = tr(cp(point(f.first, (s+2)%4)), move_to_canonical);
+    const Bare_point mp2 = tr(cp(point(f.first, (s+3)%4)), move_to_canonical);
+    const Triangle t = ct(mp0, mp1, mp2);
+
+    return t;
   }
 
   // Warning: This is a periodic version that computes the smallest possible