如何在 TikZ 中绘制破碎/无限的六边形

Question

我正在尝试获取如下图片

我目前拥有的

\begin{tikzpicture}


        \node (pol) [draw, thick, blue!90!black,rotate=90,minimum size=2.5cm,regular polygon, regular polygon sides=7] at (0,0) {}; 

        \foreach \n [count=\nu from 0, remember=\n as \lastn, evaluate={\nu+\lastn}] in {1,2,3,4,5,6,7} 
        \node[anchor=\n*(360/7)]at(pol.corner \n){$\omega_{\nu}$};
    \end{tikzpicture}

这得出

Answer 1

我不会制作六边形，而是制作七边形，但不会绘制其中一个节点。

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[dot/.style={draw,fill,circle,inner sep=1pt}]
  \foreach \l [count=\n] in {0,1,2,3,{},n-2,n-1} {
    \pgfmathsetmacro\angle{90-360/7*(\n-1)}
    \ifnum\n=5
      \coordinate (n\n) at (\angle:1);
    \else
      \node[dot,label={\angle:$\l$}] (n\n) at (\angle:1) {};
    \fi
  }
  \draw (n6) -- (n7) -- (n1) -- (n2) -- (n3) -- (n4);
  \draw[dashed,shorten >=5pt] (n4) -- (n5);
  \draw[dashed,shorten >=5pt] (n6) -- (n5);
\end{tikzpicture}

\end{document}

Answer 2

我可能会尝试类似的事情。

\documentclass[tikz,border=3mm]{standalone}
\begin{document}
\begin{tikzpicture}
\foreach \X/\Y [count=\Z] in {-60/3,-10/2,40/1,90/0,140/{$n-1$},190/{$n-2$}}
{\path (0,0) -- (\X:2.5) coordinate[pos=0.75] (C\Z)
node[anchor={180+\X},pos=0.85]{\Y};
\fill (C\Z) circle (2pt);}
\foreach \X [count=\Y] in {2,...,6}
{\draw (C\X) -- (C\Y);}
\draw[dashed,thick, shorten >=0.6cm] (-60:{2.5*0.75}) -- (-110:{2.5*0.75}); 
\draw[dashed,thick, shorten >=0.6cm] (-170:{2.5*0.75}) -- (-120:{2.5*0.75}) ;
\end{tikzpicture}
\end{document}

更新：修复了 Henri Menke 报告的一个错误，并使内容与 OP 的图片更加相似。

Answer 3

这是一个使用“正七边形”节点的解决方案。

\documentclass[tikz,border=7pt]{standalone}
\usetikzlibrary{shapes.geometric}
\tikzset{
  heptagon/.style={
    shape=regular polygon, regular polygon sides=7,
    outer sep=0, minimum size=3cm, rotate=4*360/7,
    draw, dashed
  }
}
\begin{document}
  \begin{tikzpicture}
    \draw node[heptagon](H){} (H.corner 1)
      foreach[count=\i] \x in {3,...,0,n-2,n-1}{--(H.corner \i) node[scale=3]{.}[scale=1.3]node{\x}};
    \fill[white] (H.corner 7) circle(.4);
  \end{tikzpicture}
\end{document}