如何绘制立方体的平面对称性？

2024-5-25 • tag-icon

如何绘制立方体的平面对称性？

有人知道我是否可以用 Latex 制作这个图形吗？

我知道我可以通过以下代码制作立方体，但是我怎样才能将该计划放在中间并在其下面写上这些数字呢？

\begin{figure}
\begin{center}
\caption{A labeled cube}
\begin{tikzpicture}\label{f1}
\foreach \n/\x/\l/\p in{
1/{( 0  , 0)}/{$3$}/below,
2/{( 4, 0)}/{$4$}/below,
3/{( .8, 1)}/{$7$}/south east,
4/{( 4.8, 1)}/{$8$}/right,
5/{( 0, 4)}/{$1$}/left,
6/{( 4, 4)}/{$2$}/south west,
7/{( 0.8, 4.8)}/{$5$}/above,
8/{( 4.8, 4.8)}/{$6$}/above
}
{
        \node[inner sep=2pt,circle,draw,fill,label={\p:\l}] (\n) at \x {};
    }
\draw (1) -- (2) -- (6) -- (5) -- (1);
\draw (5) -- (6) -- (8) -- (7) -- (5);
\draw (2) -- (4) -- (8) -- (6) -- (2);
\draw[dashed] (1) -- (3) -- (4);
\draw[dashed] (3) -- (7);
\end{tikzpicture}
\end{center}
\end{figure}

答案1

我擅自修改了节点的名称，以便名称与标签匹配。然后，使用的库calc，TikZ您可以通过将中间平面定位在两个相应顶点的中间来绘制中间平面，然后使用库对其进行哈希处理patterns。然后，下面的数字相对于立方体放置，但您可以决定将坐标更改为您喜欢的任何坐标。

\documentclass{standalone}

\usepackage{tikz}
    \usetikzlibrary{calc}
    \usetikzlibrary{patterns}

\begin{document}
    
    \begin{tikzpicture}
    
        \foreach \n/\x/\l/\p in{
            1/{(0, 4)}/{$1$}/left,
            2/{(4, 4)}/{$2$}/south west,
            3/{(0, 0)}/{$3$}/below,
            4/{(4, 0)}/{$4$}/below,
            5/{(0.8, 4.8)}/{$5$}/above,
            6/{(4.8, 4.8)}/{$6$}/above,
            7/{(.8, 1)}/{$7$}/south east,
            8/{(4.8, 1)}/{$8$}/right
        }{
            \node[inner sep=2pt,circle,draw,fill,label={\p:\l}] (\n) at \x {};
        }
        \draw (1.center) -- (2.center) -- (4.center) -- (3.center) -- cycle;
        \draw (1.center) -- (2.center) -- (6.center) -- (5.center) -- cycle;
        \draw (2.center) -- (4.center) -- (8.center) -- (6.center) -- cycle;
        \draw (3) -- (1) -- (5);
        \draw[dashed] (5) -- (7) -- (3);
        \draw[dashed] (7) -- (8);
        
        \draw[pattern=north west lines] ($(1)!0.5!(3)$) -- ($(5)!0.5!(7)$) -- ($(6)!0.5!(8)$) -- ($(2)!0.5!(4)$) -- cycle;
        
        \node (a1) at ($(3)!0.5!(4) - (0,0.5)$) {$1\rightarrow3$};
        \node (a2) at ($(a1) - (0,0.5)$) {$5\rightarrow7$};
        \node (a3) at ($(a2) - (0,0.5)$) {$6\rightarrow8$};
        \node (a4) at ($(a3) - (0,0.5)$) {$2\rightarrow4$};
    
    \end{tikzpicture}
    
\end{document}

得出的结果是：

编辑

按照Torbjørn T.的评论，确实更容易用一个节点替换最后四个节点

\node[below] at ($(3)!0.5!(4) - (0, 0.2)$) {$\begin{gathered} 1\to 3 \\ 5 \to 7 \\ 6 \to 8 \\ 2 \to 5 \end{gathered}$};

我仍然定义相对于节点 3 和 4 的坐标的原因是因为使用current bounding box.south坐标将使箭头位于节点 3 和节点 8 的横坐标之间，而不是位于节点 3 和 4 之间，从美学角度来说我更喜欢后者，但这只是我的品味而已。

编辑2

节点center用于cycle正常工作，如答案所示这个问题。

答案2

另一个更快的可能性是使用经过适当修改的外部工具提供的代码马查：

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}

\usepackage{tikz}
\usetikzlibrary{patterns}

\usepackage{graphicx}
\tikzset{
pattern size/.store in=\mcSize, 
pattern size = 5pt,
pattern thickness/.store in=\mcThickness, 
pattern thickness = 0.3pt,
pattern radius/.store in=\mcRadius, 
pattern radius = 1pt}
\makeatletter
\pgfutil@ifundefined{pgf@pattern@name@_s15avq03h}{
\pgfdeclarepatternformonly[\mcThickness,\mcSize]{_s15avq03h}
{\pgfqpoint{0pt}{0pt}}
{\pgfpoint{\mcSize+\mcThickness}{\mcSize+\mcThickness}}
{\pgfpoint{\mcSize}{\mcSize}}
{
\pgfsetcolor{\tikz@pattern@color}
\pgfsetlinewidth{\mcThickness}
\pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
\pgfpathlineto{\pgfpoint{\mcSize+\mcThickness}{\mcSize+\mcThickness}}
\pgfusepath{stroke}
}}
\makeatother

\begin{document}
\begin{figure}[htbp]
\centering

\tikzset{every picture/.style={line width=0.75pt}} %set default line width to 0.75pt        
\begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-1,xscale=1]
\draw   (51.5,111.59) -- (119.09,44) -- (268.5,44) -- (268.5,190.07) -- (200.91,257.67) -- (51.5,257.67) -- cycle ; \draw   (268.5,44) -- (200.91,111.59) -- (51.5,111.59) ; \draw   (200.91,111.59) -- (200.91,257.67) ;
%Straight Lines [id:da19543087105562518] 
\draw  [dash pattern={on 4.5pt off 4.5pt}]  (119.09,44) -- (119.5,189.99) ;
%Straight Lines [id:da47003768107339416] 
\draw  [dash pattern={on 4.5pt off 4.5pt}]  (119.5,189.99) -- (268.5,190.07) ;
%Straight Lines [id:da9239497588287866] 
\draw  [dash pattern={on 4.5pt off 4.5pt}]  (51.5,257.67) -- (119.5,189.99) ;
%Shape: Parallelogram [id:dp8851996353080123] 
\draw  [pattern=_s15avq03h,pattern size=6pt,pattern thickness=0.75pt,pattern radius=0pt, pattern color={rgb, 255:red, 0; green, 0; blue, 0}] (118.88,126.67) -- (267.5,126.67) -- (201.12,191.67) -- (52.5,191.67) -- cycle ;
% Text Node
\draw (36,104.07) node [anchor=north west][inner sep=0.75pt]    {$1$};
% Text Node
\draw (39.5,263.07) node [anchor=north west][inner sep=0.75pt]    {$3$};
% Text Node
\draw (202.91,261.07) node [anchor=north west][inner sep=0.75pt]    {$4$};
% Text Node
\draw (121.5,193.39) node [anchor=north west][inner sep=0.75pt]    {$7$};
% Text Node
\draw (121.09,47.4) node [anchor=north west][inner sep=0.75pt]    {$5$};
% Text Node
\draw (270.5,47.4) node [anchor=north west][inner sep=0.75pt]    {$6$};
% Text Node
\draw (207,104.99) node [anchor=north west][inner sep=0.75pt]    {$2$};
% Text Node
\draw (270.5,193.47) node [anchor=north west][inner sep=0.75pt]    {$8$};
\end{tikzpicture}
$\begin{matrix}
1\to 3& \\
5\to 7& \\
6\to 8& \\
2\to 4
\end{matrix}$
\caption{bla bla bla}
\end{figure}

\end{document}

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