$
\begin{tikzpicture}[baseline]
 \node (S) [circle,draw] {$^\star S$};
 \draw (S.135) node[left] {$\star$}.. controls +(135:3mm) and +(90:3mm) .. (S.90);
 \draw (S.45) -- +(45:3mm);
 \draw (S.0) -- +(0:3mm);
 \draw (S.-45) node [below] {$\cdot$};
  \draw (S.-90) node [below] {$\cdot$};
 \draw (S.-135) node [below] {$\cdot$};
 \draw (S.180) -- +(180:3mm);
\end{tikzpicture}
%=
%\begin{tikzpicture}[baseline]
% \node[xshift=2cm] (S') [circle,draw] {$^\star S$};
% \draw (S'.135) node[left] {$\star$} -- +(135:3mm);
% \draw (S'.90) .. controls  +(90:3mm) and + (45:3mm) .. (S'.45);
% \draw (S'.0) -- +(0:3mm);
% \draw (S'.-45) node [below] {$\cdot$};
%  \draw (S'.-90) node [below] {$\cdot$};
% \draw (S'.-135) node [below] {$\cdot$};
% \draw (S'.180) -- +(180:3mm);
%\end{tikzpicture}
= 0
$