\documentclass[11pt]{report}
\input{header}
\pagestyle{empty}
\begin{document}
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  %
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  %
  \path [halfedge] (r) edge (s);
  \path [halfedge] (s) edge (r);
  \draw [blue] (r)--(t);
  \path [halfedge] (r) edge (t);
  \path [halfedge] (t) edge (r);
  %
  \path [halfedge] (b) edge (a);
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  \path [halfedge] (1) edge (c);
  \path [halfedge,shorten <=4pt] (g) edge (f);
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  \draw [halfedge] (2) to node[sloped,below=-1pt]{$e'$} (1);
  %
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  \node at (8.5,9.5){$f_2$};
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  \node at (4.5,5.6){$f_4$};
  %
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  %
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  \path [halfedge] (f) edge (a);
\end{tikzpicture}%
\end{document}
