如何绘制具有彩色面且右上角 xyz 轴较小的交换立方体图

Question

我正在寻找一个包，在其中我可以绘制这个顶点和边标记的交换立方体图，该立方体图具有彩色（和标记）的底部（灰色）和顶部（条纹灰色）面，并且右上角有一个小的 xyz 轴，类似于这样（请原谅我的图像如此糟糕）：

以下是迄今为止我尝试过的软件包：

• Paul Taylor 的diagrams软件包。我一直用它来绘制更简单的交换图。但是，这个软件包似乎没有提供太多灵活性或高级功能。特别是，我无法用它们给面着色，也无法像我的图片那样使右上角 xyz 轴的箭头变小。

• tikz-cd。我在这个包上取得了一些进展（请参阅下面我以前的尝试和 Sebastiano 的出色回答）。但是，正如 Sebastiano 在他的回答的评论中所说，这个包似乎也无法在右上角的 xyz 轴上绘制小箭头。

问题：

有没有一个包可以让我绘制这个图表（带有小的右上角 xyz 箭头，就像上图一样？）

也许可以使用tikz? 来完成此操作？但我对此完全不熟悉。:(

任何帮助都将非常感激。

---

我的 TikZ-cd 尝试：所以我找到了这个线程tikz-cd：交换立方体的阴影面这很有帮助。但是，到目前为止，我只能使用 为没有 xyz 轴的交换立方体的顶面和底面着色tikz-cd，如下所示

使用代码：

\documentclass{article}

\usepackage{tikz-cd}

\definecolor{grey1}{RGB}{71,71,71}
\definecolor{grey2}{RGB}{100,100,100}


\begin{document}


\begin{tikzcd}[execute at end picture={
\foreach \Valor/\Nombre in   
{
  tikz@f@1-1-1/a,tikz@f@1-2-2/b,tikz@f@1-1-3/c,tikz@f@1-2-4/d,
  tikz@f@1-3-1/e,tikz@f@1-4-2/f,tikz@f@1-3-3/g,tikz@f@1-4-4/h
}
{
\coordinate (\Nombre) at (\Valor);
}
\fill[grey1,opacity=0.3] 
  (b) -- (a) -- (c) -- (d) -- cycle;
\fill[grey2,opacity=0.3] 
  (f) -- (e) -- (g) -- (h) -- cycle;
  }
]
A \arrow[rr,"f"] \arrow[dr,swap,"a"] \arrow[dd,swap,"h"] &&
  B \arrow[dd,swap,"h'" near start] \arrow[dr,"b"] \\
& A' \arrow[rr,crossing over,"f'" near start] &&
  B' \arrow[dd,"k'"] \\
C \arrow[rr,"g" near end] \arrow[dr,swap,"c"] && D \arrow[dr,swap,"d"] \\
& C' \arrow[rr,"g'"] \arrow[uu,<-,crossing over,"k" near end]&& D'
\end{tikzcd}

\end{document}

但我似乎找不到办法

1. 用条纹灰色为顶面着色。
2. 绘制右角小 xyz 轴。

有没有办法完成这个图表？

Answer 1

一次“纯粹”的tikz-cd尝试：

\documentclass{article}

\usepackage{tikz-cd}
\usetikzlibrary{patterns}

\definecolor{grey1}{RGB}{71,71,71}
\definecolor{grey2}{RGB}{100,100,100}


\begin{document}


\begin{tikzcd}[arrows=dash,execute at end picture={
\foreach \Valor/\Nombre in
{
  tikz@f@1-1-4/a,tikz@f@1-2-5/b,tikz@f@1-1-6/c,tikz@f@1-2-7/d,
  tikz@f@1-3-4/e,tikz@f@1-4-5/f,tikz@f@1-3-6/g,tikz@f@1-4-7/h%
}
{
\coordinate (\Nombre) at (\Valor);
}
\fill[pattern=north east lines,pattern color=grey1,opacity=0.3]
  (b) -- (a) -- (c) -- (d) -- cycle;
\fill[grey2,opacity=0.3]
  (f) -- (e) -- (g) -- (h) -- cycle;
  }
]
{} \arrow[r,-latex,start anchor=center] \arrow[dr,-latex,start anchor=center] \arrow[d,-latex,start anchor=center] & x && 
  A \arrow[rr,"f"] \arrow[dr,swap,"a"] \arrow[dd,swap,"h"] &&
  B \arrow[dd,swap,"h'" near start] \arrow[dr,"b"] \\
y & z &&
& A' \arrow[rr,crossing over,"f'" near start] &&
  B' \arrow[dd,"k'"] \\
&&& C \arrow[rr,"g" near end] \arrow[dr,swap,"c"] && D \arrow[dr,swap,"d"] \\
&&& & C' \arrow[rr,"g'"] \arrow[uu,crossing over,"k" near end]&& D'
\end{tikzcd}

\end{document} 

1. 用条纹灰色为顶面着色。

   为此，我加载了patterns库并使用

   \fill[pattern=north east lines,pattern color=grey1,opacity=0.3]
   

2. 绘制右角小 xyz 轴。

   为此，我使用了一个空节点{}并添加了start anchor=center箭头，如下所示

   \arrow[r,-latex,start anchor=center]
   

如果你想隐藏箭头之间不可见的部分B，D你可以使用类似

\arrow[dd,swap,start anchor={[yshift=-25pt]},"h'"]

获得

---

编辑

如果您想要立方体中的箭头，只需删除环境arrows=dash中的选项tikzcd（或将其替换arrows=-latex为）：

\documentclass{article}

\usepackage{tikz-cd}
\usetikzlibrary{patterns}

\definecolor{grey1}{RGB}{71,71,71}
\definecolor{grey2}{RGB}{100,100,100}


\begin{document}


\begin{tikzcd}[execute at end picture={
\foreach \Valor/\Nombre in
{
  tikz@f@1-1-4/a,tikz@f@1-2-5/b,tikz@f@1-1-6/c,tikz@f@1-2-7/d,
  tikz@f@1-3-4/e,tikz@f@1-4-5/f,tikz@f@1-3-6/g,tikz@f@1-4-7/h%
}
{
\coordinate (\Nombre) at (\Valor);
}
\fill[pattern=north east lines,pattern color=grey1,opacity=0.3]
  (b) -- (a) -- (c) -- (d) -- cycle;
\fill[grey2,opacity=0.3]
  (f) -- (e) -- (g) -- (h) -- cycle;
  }
]
{} \arrow[r,-latex,start anchor=center] \arrow[dr,-latex,start anchor=center] \arrow[d,-latex,start anchor=center] & x &&
  A \arrow[rr,"f"] \arrow[dr,swap,"a"] \arrow[dd,swap,"h"] &&
  B \arrow[dd,swap,"h'" near start] \arrow[dr,"b"] \\
y & z &&
& A' \arrow[rr,crossing over,"f'" near start] &&
  B' \arrow[dd,"k'"] \\
&&& C \arrow[rr,"g" near end] \arrow[dr,swap,"c"] && D \arrow[dr,swap,"d"] \\
&&& & C' \arrow[rr,"g'"] \arrow[uu,<-,crossing over,"k" near end]&& D'
\end{tikzcd}

\end{document} 

Answer 2

作为记录，有可能的使用这种方法缩短 xyz 轴：

shorten >= ...pt基于karlkoeller 的回答，我们只需要使用

\documentclass{article}

\usepackage{tikz-cd}
\usetikzlibrary{patterns}

\definecolor{grey1}{RGB}{71,71,71}
\definecolor{grey2}{RGB}{100,100,100}

\begin{document}

\begin{tikzcd}[execute at end picture={
\foreach \Valor/\Nombre in
{
  tikz@f@1-1-4/a,tikz@f@1-2-5/b,tikz@f@1-1-6/c,tikz@f@1-2-7/d,
  tikz@f@1-3-4/e,tikz@f@1-4-5/f,tikz@f@1-3-6/g,tikz@f@1-4-7/h%
}
{
\coordinate (\Nombre) at (\Valor);
}
\fill[pattern=north east lines,pattern color=grey1,opacity=0.3]
  (b) -- (a) -- (c) -- (d) -- cycle;
\fill[grey2,opacity=0.3]
  (f) -- (e) -- (g) -- (h) -- cycle;
  }
]
{} \arrow[r,shorten >= 10pt,-latex,start anchor=center] \arrow[dr,shorten >=     20pt,-latex,start anchor=center] \arrow[d,shorten >= 12pt,-latex,start anchor=center] & x && 
  A \arrow[rr,"f"] \arrow[dr,swap,"a"] \arrow[dd,swap,"h"] &&
  B \arrow[dd,swap,"h'" near start] \arrow[dr,"b"] \\
y & z 
&&
& A' \arrow[rr,crossing over,"f'" near start] &&
  B' \arrow[dd,"k'"] \\
&&& C \arrow[rr,"g" near end] \arrow[dr,swap,"c"] && D \arrow[dr,swap,"d"] \\
&&& & C' \arrow[rr,"g'"] \arrow[uu,<-,crossing over,"k" near end]&& D'
\end{tikzcd}
\end{document}