diff --git a/Triangulation_3/include/CGAL/Triangulation_3/internal/Triangulation_segment_traverser_3_impl.h b/Triangulation_3/include/CGAL/Triangulation_3/internal/Triangulation_segment_traverser_3_impl.h
index f7411f652e8..4a5304a6757 100644
--- a/Triangulation_3/include/CGAL/Triangulation_3/internal/Triangulation_segment_traverser_3_impl.h
+++ b/Triangulation_3/include/CGAL/Triangulation_3/internal/Triangulation_segment_traverser_3_impl.h
@@ -575,7 +575,7 @@ Triangulation_segment_cell_iterator_3<Tr,Inc>::walk_to_next_3(const Simplex& pre
                         return std::make_pair(prev_after_walk, cur_after_walk);
                     }
                 }
-                CGAL_triangulation_assertion( false );
+                CGAL_unreachable();
                 return std::make_pair(prev, cur);
             case 1:
                 if(regular_case)
@@ -593,10 +593,10 @@ Triangulation_segment_cell_iterator_3<Tr,Inc>::walk_to_next_3(const Simplex& pre
                         return std::make_pair(prev_after_walk, cur_after_walk);
                     }
                 }
-                CGAL_triangulation_assertion( false );
+                CGAL_unreachable();
                 return std::make_pair(prev, cur);
             default:
-                CGAL_triangulation_assertion( false );
+                CGAL_unreachable();
                 return std::make_pair(prev, cur);
         }
     }
@@ -626,8 +626,7 @@ Triangulation_segment_cell_iterator_3<Tr,Inc>::walk_to_next_3(const Simplex& pre
       prev_after_walk = Simplex( std::get<0>(cur), Tr::VERTEX, pos, -1 );
       break;
     default:
-      prev_after_walk = Simplex( std::get<0>(cur), Tr::OUTSIDE_AFFINE_HULL, -1, -1 );
-      CGAL_triangulation_assertion( false );
+      CGAL_unreachable();
     }
 
     Simplex cur_after_walk(Cell_handle(), Tr::OUTSIDE_AFFINE_HULL, -1, -1);
@@ -726,7 +725,7 @@ walk_to_next_3_inf( int inf )
                     return;
                 }
             }
-            CGAL_triangulation_assertion( false );
+            CGAL_unreachable();
             return;
         case 1:
             prev_lt() = Tr::VERTEX;
@@ -738,10 +737,10 @@ walk_to_next_3_inf( int inf )
                     return;
                 }
             }
-            CGAL_triangulation_assertion( false );
+            CGAL_unreachable();
             return;
         default:
-            CGAL_triangulation_assertion( false );
+            CGAL_unreachable();
             return;
     }
 }
@@ -1007,7 +1006,7 @@ walk_to_next_2()
                         this->li() = cell()->index( prev_cell()->vertex( prev_li() ) );
                         return;
                     default:
-                        CGAL_triangulation_assertion( false );
+                        CGAL_unreachable();
                         return;
                 }
             }
@@ -1018,7 +1017,7 @@ walk_to_next_2()
             return;
         }
         default:
-        CGAL_triangulation_assertion( false );
+        CGAL_unreachable();
     }
 }
 
diff --git a/Triangulation_3/include/CGAL/Triangulation_segment_traverser_3.h b/Triangulation_3/include/CGAL/Triangulation_segment_traverser_3.h
index 49ba25ccd3e..bc00071cb23 100644
--- a/Triangulation_3/include/CGAL/Triangulation_segment_traverser_3.h
+++ b/Triangulation_3/include/CGAL/Triangulation_segment_traverser_3.h
@@ -625,7 +625,7 @@ private:
         _curr_simplex = cell;
       break;
     default:
-      CGAL_assertion(false);
+      CGAL_unreachable();
     };
   }
 
@@ -719,7 +719,7 @@ public:
         break;
 
       default:
-        CGAL_assertion(false);
+        CGAL_unreachable();
       };
       break;
     }
@@ -792,7 +792,7 @@ public:
         break;
       }
       default:
-        CGAL_assertion(false);//should not happen
+        CGAL_unreachable();//should not happen
       };
       break;
     }
@@ -863,7 +863,7 @@ public:
             Cell_handle ec;
             int ei = -1, ej = -1;
             if (!triangulation()->is_edge(get_vertex(), chnext->vertex(linext), ec, ei, ej))
-              CGAL_assertion(false);
+              CGAL_unreachable();
             _curr_simplex = Edge(ec, ei, ej);
           }
         }
@@ -916,7 +916,7 @@ public:
     break;
 
     default:
-      CGAL_assertion(false);
+      CGAL_unreachable();
     };
     return *this;
   }
@@ -1017,10 +1017,10 @@ private:
     case 3 ://cell
       return ch != get_cell();
     default:
-      CGAL_assertion(false);
+      CGAL_unreachable();
     }
     //should not be reached
-    CGAL_assertion(false);
+    CGAL_unreachable();
     return false;
   }
 
@@ -1074,7 +1074,7 @@ private:
       return v1b;
 
     std::cerr << "There is no vertex shared by e1 and e2" << std::endl;
-    CGAL_assertion(false);
+    CGAL_unreachable();
     return Vertex_handle();
   }
 
@@ -1100,7 +1100,7 @@ private:
     } while (++circ != end);
 
     std::cerr << "There is no facet shared by e1 and e2" << std::endl;
-    CGAL_assertion(false);
+    CGAL_unreachable();
     return Facet(Cell_handle(), 0);
   }
 
@@ -1118,7 +1118,7 @@ private:
     } while (++circ != end);
 
     std::cerr << "There is no facet shared by e and v" << std::endl;
-    CGAL_assertion(false);
+    CGAL_unreachable();
     return Facet(Cell_handle(), 0);
   }
 
@@ -1135,7 +1135,7 @@ private:
     } while (++circ != end);
 
     std::cerr << "There is no cell shared by e and v" << std::endl;
-    CGAL_assertion(false);
+    CGAL_unreachable();
     return Cell_handle();
   }