\documentclass[tikz]{standalone}

\usetikzlibrary{decorations.pathreplacing,decorations.markings}
\usetikzlibrary{patterns}

\standaloneconfig{margin=12pt}

\begin{document}

\begin{tikzpicture}

% sets up command for arrows in the middle of arcs
\tikzset{->-/.style={decoration={
  markings,
  mark=at position #1 with {\arrow{>}}},postaction={decorate}}}

%draw vertices and orbifold point
\draw[fill=black] (0,0) circle [radius=2pt];
\draw[fill=black] (0,1.5) circle [radius=2pt];
\draw[thick] (0,0.75) node {$\mathbf{\times}$};
\draw[fill=black] (-0.65,0.75) circle [radius=2pt];

%draw interior arcs
%\draw (0,0) to (0,0.75);
\draw[out=45,in=0] (0,0) to (0,1);
\draw[out=180,in=135] (0,1) to (0,0);
\draw[in=30,looseness=3] (-0.65,0.75) to (0,0);

%draw exterior boundaries
\draw[out=0,in=0,looseness=1.5] (0,0) to (0,1.5);
\draw[out=180,in=-180,looseness=1.5] (0,0) to (0,1.5);

%vertex labels
\node[above,scale=0.75] at (0,1.5) {$v_2$};
\node[below,scale=0.75] at (0,0) {$v_1$};
\node[left,scale=0.75] at (-0.65,0.75) {$v_3$};

\end{tikzpicture}

\end{document}