其中一条边进入了顶点 1 的圆，如何纠正

Question

在下面的代码中，其中一条边进入顶点 1 的圆。如何修改此代码。

\documentclass[tikz,margin=5pt]{standalone}

\begin{document}
\begin{tikzpicture} 
\foreach \n [count=\i] in {3,4,5} {
    \pgfmathsetmacro{\nfold}{360/\n}
    \begin{scope}[xshift=5*\i cm]
    \begin{scope}[rotate=-60-\nfold]
    \foreach \rot in {1,2,...,\n} { 
        \pgfmathsetmacro{\next}{\rot*\nfold +\nfold}
        \draw[very thick] (\next:1.5)  --(\rot*\nfold:1.5);
        \draw[black,fill=black]  (\rot*\nfold:1.5) circle (0.08);
        \node[inner sep=1pt, fill=white, circle, draw=black] at (\rot*\nfold:1.5) {\rot}; 
    }
      \end{scope}
    \node[below] at (0,-2.) {$C_{\n}$};
    \end{scope}
}
\end{tikzpicture}
\end{document}

Answer 1

\documentclass[tikz, border=1cm]{standalone}
\begin{document}
\begin{tikzpicture} 
\foreach \n [count=\i] in {3,4,5}{
\pgfmathsetmacro{\nfold}{360/\n}
\begin{scope}[xshift=5*\i cm]
\begin{scope}[rotate=-60-\nfold]
\foreach \rot in {1,2,...,\n} 
  \draw[very thick] (\rot*\nfold+\nfold:1.5) -- (\rot*\nfold:1.5);
\foreach \rot in {1,2,...,\n}
  \node[inner sep=1pt, fill=white, circle, draw] at (\rot*\nfold:1.5) {\rot}; 
\end{scope}
\node[below] at (0,-2.) {$C_{\n}$};
\end{scope}
}
\end{tikzpicture}
\end{document}