难度较大的六角链

Question

我正在尝试绘制这个六边形的路径图，但它从某个六边形开始断开，然后延续到下一个六边形。

我知道如何创建六边形路径图并创建了断开的路径图，但我不确定如何向图中添加虚线并标记顶点，因为我只能创建一个垂直链然后旋转 90 度（或者我必须旋转每个六边形，以便边可以对齐而不是顶点）。

有谁知道我该如何用虚线和断开的六边形来创建这个吗？在阅读了有关使用 tikz 在 latex 中创建形状的内容后，我仍然不确定如何创建这些。照片是在 word 文档上创建的链条。

非常感谢你的帮助

Answer 1

因为这是一张“重复”的图片，所以我们用循环来重复\foreach。首先放置一些坐标，然后绘制线条、圆圈（顶点）和标签。

像这样：

\documentclass[tikz,border=2mm]{standalone}

\begin{document}
\begin{tikzpicture}[thick,scale=1.5]
% coordinates
\foreach\i in {0,...,12}
{
  \coordinate (A\i) at ({0.5*sqrt(3)*\i},{1+0.5*mod(\i,2)}); % top
  \coordinate (B\i) at ({0.5*sqrt(3)*\i}, {-0.5*mod(\i,2)}); % bottom
}
% left hexagons
\draw (A6) foreach\i in {6,...,0} {-- (A\i)} -- (B0) foreach\i in {1,...,6} {-- (B\i)};
\foreach\i in {2,4,6}
  \draw (A\i) -- (B\i);
% right hexagon
\draw (A10) -- (A11) -- (A12) -- (B12) -- (B11) -- (B10) -- cycle;
% dashed lines
\foreach\i in {A,B}\foreach\j in {6,9}
  \pgfmathtruncatemacro\k{\j+1}
  \draw[gray,dotted] (\i\j) -- (\i\k);
\draw  [gray,dotted] (A7)   ++ (0.2,-1) --++ ({sqrt(3)-0.4},0);
% vertices and labels
\foreach\i in {0,...,7,9,10,11,12}
{
  \pgfmathtruncatemacro\j{\i+1}
  \draw[fill=white] (A\i) circle (0.4mm) \ifnum\i<3 node[above] {$\j$}\fi;
  \pgfmathtruncatemacro\j{6-\i}
  \draw[fill=white] (B\i) circle (0.4mm) \ifnum\i<3 node[below] {$\j$}\fi;
}
\node[yshift=5mm]    at (A10) {$2n-3$};
\node[above]         at (A11) {$2n-4$};
\node[above right]   at (A12) {$2n+1$};
\node[below right]   at (B12) {$2n$};
\node[below]         at (B11) {$2n-1$};
\node[yshift=-5mm]   at (B10) {$2n-2$};
\foreach\i in {1,2,3}
  \pgfmathtruncatemacro\j{2*\i-1}
  \node[yshift=-1cm] at (B\j) {\Large$H_\i$};
\node[yshift=-1cm]   at (B7)  {\Large$\cdots$};
\node[yshift=-1cm]   at (B9)  {\Large$\cdots$};
\node[yshift=-1cm]   at (B11) {\Large$H_n$};
\end{tikzpicture}
\end{document}

Answer 2

带chemfig包装

\documentclass[border=1.5cm]{standalone}
\usepackage{chemfig}
\def\atsep{4em}
\begin{document}
    \chemfig[atom sep=\atsep]{
        *6(--(*6(--(*6(--(*6(--[,,,,draw=none](*6(-[,,,,draw=none]-(*6(-----))---[,,,,draw=none]))-[,,,,draw=none]-[,,,,draw=none]-))---))---))----)
    }
    \chemmove{
        \coordinate (R1) at (cyclecenter1);
        \coordinate (R2) at (cyclecenter2);
        \coordinate (R3) at (cyclecenter3);
        \coordinate (R4) at (cyclecenter4);
        \coordinate (R5) at (cyclecenter5);
        \coordinate (R6) at (cyclecenter6);
        \draw[-, dashed, shorten <=10pt, shorten >=10pt] (R4) -- (R5);
        \foreach \x in {1,2,3,6}{\foreach \y in {30,90,...,330}{
            \draw[fill=white] (R\x) ++(\y:\atsep) circle[radius=2pt];}}
        \foreach \x in {4,5}{\foreach \y in {90,270}{
                \draw[fill=white] (R\x) ++(\y:\atsep) circle[radius=2pt];}}
        \path[every node/.style={circle, label distance=-0.5em}]
            (R1) ++(150:\atsep) node[label={150:1}] {}
            (R1) ++(90:\atsep) node[label={90:2}] {}
            (R1) ++(30:\atsep) node[label={90:3}] {}
            (R1) ++(-30:\atsep) node[label={270:4}] {}
            (R1) ++(-90:\atsep) node[label={-90:5}] {}
            (R1) ++(-150:\atsep) node[label={-150:6}] {}
            (R1) ++(-90:3em+\atsep) node {$\mathrm{H}_1$}
            (R2) ++(-90:3em+\atsep) node {$\mathrm{H}_2$}
            (R6) ++(-90:3em+\atsep) node {$\mathrm{H}_n$};
        \path[every node/.style={label distance=-0.5em}]
            (R6) ++(30:\atsep) node[label={30:$2n+1$}] {}
            (R6) ++(90:\atsep) node[label={90:$2n-4$}] {}
            (R6) ++(150:\atsep) node[label={[label distance=0.3em]90:$2n-3$}] {}
            (R6) ++(-150:\atsep) node[label={[label distance=0.3em]-90:$2n-2$}] {}
            (R6) ++(-90:\atsep) node[label={-90:$2n-1$}] {}
            (R6) ++(-30:\atsep) node[label={-30:$2n$}] {};
        }
\end{document}

Answer 3

另一种解决方案是使用regular polygons及其锚点作为参考。

\documentclass[tikz, border=2mm]{standalone}
\usetikzlibrary{shapes.geometric, positioning}

\begin{document}
\begin{tikzpicture}[
    hexagon/.style={regular polygon, regular polygon sides=6, shape border rotate=30, draw, minimum size=3cm, outer sep=0pt}]

    \node[hexagon, label={[label distance=5mm]below:$H_1$}] (h1) {};
    \node[hexagon, label={[label distance=5mm]below:$H_2$}, right=-.25\pgflinewidth of h1.side 5] (h2) {};
    \node[hexagon, label={[label distance=5mm]below:$H_3$}, right=-.25\pgflinewidth of h2.side 5] (h3) {};
    \node[hexagon, right=-.25\pgflinewidth of h3.side 5, draw=none] (h4) {};
    \node[hexagon, right=-.25\pgflinewidth of h4.side 5, draw=none] (h5) {};
    \node[hexagon, label={[label distance=5mm]below:$H_n$}, right=-.25\pgflinewidth of h5.side 5] (h6) {};
    \draw[dotted] (h4.corner 2)--(h4.corner 1);
    \draw[dotted] (h4.corner 3)--(h4.corner 4);
    \draw[dotted] (h5.corner 1)--(h5.corner 6);
    \draw[dotted] (h5.corner 4)--(h5.corner 5);
    \foreach \i in {1,2,...,6}
        \foreach \j in {1,2,3,6}
            \draw[fill=white] (h\j.corner \i) circle (2pt);
    \foreach \i/\j in {4/1, 4/4, 5/1, 5/4}
        \draw[fill=white] (h\i.corner \j) circle(2pt);
    \foreach \i in {-5pt, 0pt, 5pt}
        \draw[fill] ([xshift=\i]h4.side 5) circle(1pt);
    \foreach \i/\j in {1/2,2/1,3/6}
        \node[above=1mm] at (h1.corner \j) {\i};
    \foreach \i/\j in {$2n-3$/2,$2n-4$/1,$2n+1$/6}
        \node[above=1mm] at (h6.corner \j) {\i};
    \foreach \i/\j in {4/5,5/4,6/3}
        \node[below=1mm] at (h1.corner \j) {\i};
    \foreach \i/\j in {$2n$/5,$2n-1$/4,$2n-2$/3}
        \node[below=1mm] at (h6.corner \j) {\i};
\end{tikzpicture}
\end{document}