  bool operator() (SFace_handle sf1, SFace_handle sf2) const {
    CGAL_NEF_TRACEN("sort sfaces");
    if(&*sf1 == &*sf2) return false;

    sort_vertices<T> SORT(*this->sncp());

    CGAL_NEF_TRACEN("  vertices " << sf1->center_vertex()->point() << " , " << sf2->center_vertex()->point());
    if(sf1->center_vertex() != sf2->center_vertex())
      return SORT(sf1->center_vertex(), sf2->center_vertex());

    //    sort_sface_cycle_entries<Base> sort_cycles((Base) *this);
    //    return sort_cycles(*sf1->sface_cycles_begin(), *sf2->sface_cycles_begin());

    SM_decorator SD(&*sf1->center_vertex());
    moreLeft<Base> ml((Base) *this);
    Vector_3 plus(1,0,0);

    SFace_cycle_iterator fc;

    CGAL_NEF_TRACEN("  sface 1");

    SHalfedge_handle se1;
    SHalfloop_handle sl1;
    CGAL_forall_sface_cycles_of(fc,sf1) {
      if(fc.is_shalfedge()) {
        SHalfedge_handle se(fc);
        SHalfedge_around_sface_circulator ec(se),ee(se);
        CGAL_For_all(ec,ee) {
          CGAL_NEF_TRACEN("     " << ec->source()->point() <<
                 " | " << ec->circle().orthogonal_vector());
          if(ml(ec, se1) == -1)
            se1 = ec;
        }
      }
      else if(fc.is_shalfloop())
        sl1 = SHalfloop_handle(fc);
      else
        CGAL_assertion(fc.is_svertex());
    }

    CGAL_NEF_TRACEN("  sface 2");

    SHalfedge_handle se2;
    SHalfloop_handle sl2;
    CGAL_forall_sface_cycles_of(fc,sf2) {
      if(fc.is_shalfedge()) {
        SHalfedge_handle se(fc);
        SHalfedge_around_sface_circulator ec(se),ee(se);
        CGAL_For_all(ec,ee) {
          CGAL_NEF_TRACEN("     " << ec->source()->point() <<
                 " | " << ec->circle().orthogonal_vector());
          if(ml(ec, se2) == -1)
            se2 = ec;
        }
      }
      else if(fc.is_shalfloop())
        sl2 = SHalfloop_handle(fc);
      else
        CGAL_assertion(fc.is_svertex());
    }

    CGAL_NEF_TRACEN("  sedge cycles existing? " << (se1 != SHalfedge_handle())
           << " , " << (se2 != SHalfedge_handle()));

    if(se1 != SHalfedge_handle() && se2 == SHalfedge_handle())
      return true;
    if(se1 == SHalfedge_handle() && se2 != SHalfedge_handle())
      return false;

    if(se1 == SHalfedge_handle() && se2 == SHalfedge_handle()) {
      Vector_3 vec1 = sl1->circle().orthogonal_vector();
      Vector_3 vec2 = sl2->circle().orthogonal_vector();
      CGAL_NEF_TRACEN("  sloops " << vec1 << " , " << vec2);
      if(vec1.x() != vec2.x())
        return vec1.x() < vec2.x();
      else if(vec1.y() != vec2.y())
        return vec1.y() < vec2.y();
      else if(vec1.z() != vec2.z())
        return vec1.z() < vec2.z();
    }

    CGAL_assertion(se1 != SHalfedge_handle() && se2 != SHalfedge_handle());

    CGAL_NEF_TRACEN("  minimal sedge in sface 1:" << se1->source()->point() <<
           " , " << se1->circle().orthogonal_vector());
    CGAL_NEF_TRACEN("  minimal sedge in sface 2:" << se2->source()->point() <<
           " , " << se2->circle().orthogonal_vector());
    CGAL_NEF_TRACEN("result " << ml(se1,se2));
    switch(ml(se1, se2)) {
    case -1: return true;
    case  1: return false;
    }
    sort_sface_cycle_entries<T> SORTSFC(*this->sncp());
    return SORTSFC(*sf1->sface_cycles_begin(), *sf2->sface_cycles_begin());
  }
  bool operator() (SFace_handle sf1, SFace_handle sf2) const {
    CGAL_NEF_TRACEN("sort sfaces");
    if(&*sf1 == &*sf2) return false;

    sort_vertices<T> SORT(*this->sncp());

    CGAL_NEF_TRACEN("  vertices " << sf1->center_vertex()->point() << " , " << sf2->center_vertex()->point());
    if(sf1->center_vertex() != sf2->center_vertex())
      return SORT(sf1->center_vertex(), sf2->center_vertex());

     
     

    SM_decorator SD(&*sf1->center_vertex());
    moreLeft<Base> ml((Base) *this);
    Vector_3 plus(1,0,0);

    SFace_cycle_iterator fc;

    CGAL_NEF_TRACEN("  sface 1");

    SHalfedge_handle se1;
    SHalfloop_handle sl1;
    CGAL_forall_sface_cycles_of(fc,sf1) {
      if(fc.is_shalfedge()) {
        SHalfedge_handle se(fc);
        SHalfedge_around_sface_circulator ec(se),ee(se);
        CGAL_For_all(ec,ee) {
          CGAL_NEF_TRACEN("     " << ec->source()->point() <<
                 " | " << ec->circle().orthogonal_vector());
          if(ml(ec, se1) == -1)
            se1 = ec;
        }
      }
      else if(fc.is_shalfloop())
        sl1 = SHalfloop_handle(fc);
      else
        CGAL_assertion(fc.is_svertex());
    }

    CGAL_NEF_TRACEN("  sface 2");

    SHalfedge_handle se2;
    SHalfloop_handle sl2;
    CGAL_forall_sface_cycles_of(fc,sf2) {
      if(fc.is_shalfedge()) {
        SHalfedge_handle se(fc);
        SHalfedge_around_sface_circulator ec(se),ee(se);
        CGAL_For_all(ec,ee) {
          CGAL_NEF_TRACEN("     " << ec->source()->point() <<
                 " | " << ec->circle().orthogonal_vector());
          if(ml(ec, se2) == -1)
            se2 = ec;
        }
      }
      else if(fc.is_shalfloop())
        sl2 = SHalfloop_handle(fc);
      else
        CGAL_assertion(fc.is_svertex());
    }

    CGAL_NEF_TRACEN("  sedge cycles existing? " << (se1 != SHalfedge_handle())
           << " , " << (se2 != SHalfedge_handle()));

    if(se1 != SHalfedge_handle() && se2 == SHalfedge_handle())
      return true;
    if(se1 == SHalfedge_handle() && se2 != SHalfedge_handle())
      return false;

    if(se1 == SHalfedge_handle() && se2 == SHalfedge_handle()) {
      Vector_3 vec1 = sl1->circle().orthogonal_vector();
      Vector_3 vec2 = sl2->circle().orthogonal_vector();
      CGAL_NEF_TRACEN("  sloops " << vec1 << " , " << vec2);
      if(vec1.x() != vec2.x())
        return vec1.x() < vec2.x();
      else if(vec1.y() != vec2.y())
        return vec1.y() < vec2.y();
      else if(vec1.z() != vec2.z())
        return vec1.z() < vec2.z();
    }

    CGAL_assertion(se1 != SHalfedge_handle() && se2 != SHalfedge_handle());

    CGAL_NEF_TRACEN("  minimal sedge in sface 1:" << se1->source()->point() <<
           " , " << se1->circle().orthogonal_vector());
    CGAL_NEF_TRACEN("  minimal sedge in sface 2:" << se2->source()->point() <<
           " , " << se2->circle().orthogonal_vector());
    CGAL_NEF_TRACEN("result " << ml(se1,se2));
    switch(ml(se1, se2)) {
    case -1: return true;
    case  1: return false;
    }
    sort_sface_cycle_entries<T> SORTSFC(*this->sncp());
    return SORTSFC(*sf1->sface_cycles_begin(), *sf2->sface_cycles_begin());
  }