\begin{figure}[H]
  \begin{center}
     \unitlength=4pt
     \begin{picture}(20, 32)(0,-3)
     \gasset{Nw=5,Nh=5,Nmr=2.5,curvedepth=0}
     \thinlines
     \node[Nmarks=i,iangle=180](A1)(0,20){$1$}
     \node[Nmarks=f,fangle=45](A2)(20,20){$2$}
     \node(A3)(0,0){$3$}
     \node[Nmarks=f,fangle=-45](A4)(20,0){$4$}
     \drawloop[loopangle=90](A1){$b$}
     \drawedge(A2,A1){$a$}
     \drawedge(A3,A2){$b$}
     \drawedge(A1,A3){$b$}
     \drawedge[curvedepth=3](A2,A4){$a$}
     \drawedge[curvedepth=3](A4,A2){$a$}
     \drawedge[curvedepth=3](A3,A4){$b$}
     \drawedge[curvedepth=3](A4,A3){$a$}
     \end{picture}
   \end{center}
   \caption{L'automate ${\cal A}^r$.}
\end{figure}