% Figure A.2 begins

\midinsert
\medskip

\def\facei#1{\hglue10pt\smash{\hbox to 0pt{%
\hidewidth%
\lower\fontdimen22\textfont2\hbox{$#1$}%
\hidewidth%
}}\hglue10pt}

\def\xfacei#1{\hglue20pt\smash{\hbox to 0pt{%
\hidewidth%
\lower\fontdimen22\textfont2\hbox{$#1$}%
\hidewidth%
}}\hglue20pt}

\def\htedgi#1{{\hbox to 20pt{\vrule height0.5pt depth0.5pt width0pt\hss%
\smash{\hbox to 0pt{\hidewidth%
\raise 3pt\hbox{$#1$}\hidewidth}}%
\smash{\hbox to 0pt{\hidewidth%
\vrule height0.1pt width21.2pt depth0.1pt\hidewidth}}%
\hss}}}

\def\vtedgi#1{{\hbox to 1pt{\hss\vrule height10pt depth10pt width0pt%
\smash{\hbox to 0pt{\hidewidth%
\lower\fontdimen22\textfont2\hbox{$#1$\hglue10pt}\hidewidth}}%
\smash{\hbox to 0pt{\hidewidth%
\vrule height10.6pt width0.2pt depth10.6pt\hidewidth}}%
\hss}}}  

\centerline{
\vbox{\offinterlineskip
\setbox0=\hbox{\vt\htedg\vt}
\hsize=\wd0
\box0
\hbox{\vtedg\facei{+}\vtedg}
\hbox{\vt\htedg\vt}
\smallskip
\centerline{\strut(a)}
}
\hskip 30pt minus 10pt
\vbox{\offinterlineskip
\setbox0=\hbox{\vt\htedgi{+}\vt}
\hsize=\wd0
\box0
\bigskip
\centerline{\strut(b)}
}
\hskip 30pt minus 10pt
\vbox{\offinterlineskip
\hsize=20pt
\setbox0=\hbox{\facei{-}\vtedg\facei{+}\xfacei{}\facei{+}\vtedg\facei{-}}
\hsize=\wd0
\box0
\hbox{\htedg\vti{\hookrightarrow}\htedg\xfacei{=}%
\htedg\vti{\hookleftarrow}\htedg}
\hbox{\facei{+}\vtedg\facei{-}\xfacei{}\facei{-}\vtedg\facei{+}}
\smallskip
\centerline{\strut(c)}
}
}
\vskip 15pt
\centerline{
\vbox{\offinterlineskip
\hsize=20pt
\setbox0=\hbox{\pvt\phe\pvt\xfacei{}\vt\htedg\vt}
\hsize=\wd0
\box0
\hbox{\pvt\phe\pvt\xfacei{}\vtedg\facei{+}\vtedg}
\hbox{\vt\htedgi{+}\vt\xfacei{\mapsto}\vt\htedg\vt}
\hbox{\pvt\phe\pvt\xfacei{}\vtedg\facei{+}\vtedg}
\hbox{\pvt\phe\pvt\xfacei{}\vt\htedg\vt}
\smallskip
\centerline{\strut(d)}
}
\hskip 30pt minus 10pt
\vbox{\offinterlineskip
\hsize=20pt
\setbox0=\hbox{\phe\pvt\phe\xfacei{}\pvt\phe\vt\phe\pvt}
\hsize=\wd0
\box0
\hbox{\facei{-}\vtedg\facei{+}\xfacei{}\pvt\phe\vtedgi{+}\phe\pvt}
\hbox{\htedg\vti{\hookrightarrow}\htedg\xfacei{\mapsto}%
\vt\htedgi{-}\vt\htedgi{-}\vt}
\hbox{\facei{+}\vtedg\facei{-}\xfacei{}\pvt\phe\vtedgi{+}\phe\pvt}
\hbox{\phe\pvt\phe\xfacei{}\pvt\phe\vt\phe\pvt}
\smallskip
\centerline{\strut(e)}
}
}

\nobreak
\smallskip
\nobreak

\centerline{\bf Figure A.2}

\smallskip
\endinsert

% Figure A.2 ends
