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锥体的金字塔交换图

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锥体的金字塔交换图

在 Awodey 的第二版中范畴论他建议将圆锥体想象成一个多面金字塔。我很想制作正确的交换图，但我不知道如何制作多面金字塔。第一个图只是一个多面金字塔，而第二个图是两个这样的金字塔（共用同一个底座）的叠加，只是顶点不同，中间有一个箭头。

编辑：这差不多是我想要制作的第一张图表，不过我希望我的金字塔是对称的。最好是黑白的，指向顶点的垂直箭头保持为红色，金字塔表面略带蓝色（但仍然透明）。多面金字塔

第二张图会有另一个金字塔，其顶点平移到相同的高度，叠加在第一张图的金字塔上。

答案1

也许这就是你想要的？我使用了regular polygon金字塔的形状，底座有 8 个面；底座倾斜且旋转。根据您的需要调整设置：

在此处输入图片描述

代码：

\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}

\tikzset{
  mypyr/.style={
    regular polygon,
    regular polygon sides=8,
    minimum size=3cm,
    rotate=-50,
    yslant=0.5
  }
}

\begin{document}

\begin{tikzpicture}
\node[mypyr]
  (base1) at (0,0) {};
\coordinate (appex1) at (0,4); 
\foreach \Coord in {1,4,5,6,7,8}
{
  \draw (base1.corner \Coord) -- (appex1);
}
\foreach \Coord in {2,3}
{
  \draw[dashed] (base1.corner \Coord) -- (appex1);
}
\foreach \Coord in {4,...,7}
{
\fill[blue,opacity=0.2]
  (base1.corner \Coord) -- (base1.corner \the\numexpr\Coord+1\relax) -- (appex1) -- cycle;
}
\fill[blue,opacity=0.2]
  (base1.corner 8) -- (base1.corner 1) -- (appex1) -- cycle;
\node[mypyr,draw] at (0,0) {};
\foreach \Coord in {1,...,4}
{
  \draw[opacity=0.6]
   (base1.corner \Coord) -- (base1.corner \the\numexpr\Coord+4\relax);
}
\fill[orange!40,opacity=0.4]
    (base1.corner 2) -- 
    (appex1) --
    (base1.corner 6) -- cycle;
\draw[red] (0,0) -- (appex1);
\end{tikzpicture}

\begin{tikzpicture}
\node[mypyr]
  (base1) at (0,0) {};
\coordinate (appex1) at (0,4); 
\coordinate (appex2) at (-2.5,4); 
\foreach \Coord in {1,4,5,6,7,8}
{
  \draw (base1.corner \Coord) -- (appex1);
  \draw (base1.corner \Coord) -- (appex2);
}
\foreach \Coord in {2,3}
{
  \draw[dashed] (base1.corner \Coord) -- (appex1);
  \draw[dashed] (base1.corner \Coord) -- (appex2);
}
\foreach \Coord in {4,...,7}
{
\fill[blue,opacity=0.2]
  (base1.corner \Coord) -- (base1.corner \the\numexpr\Coord+1\relax) -- (appex1) -- cycle;
\fill[green,opacity=0.2]
  (base1.corner \Coord) -- (base1.corner \the\numexpr\Coord+1\relax) -- (appex2) -- cycle;
}
\fill[blue,opacity=0.2]
  (base1.corner 8) -- (base1.corner 1) -- (appex1) -- cycle;
\fill[green,opacity=0.2]
  (base1.corner 8) -- (base1.corner 1) -- (appex2) -- cycle;
\draw[red] (0,0) -- (appex1);
\draw[red] (0,0) -- (appex2);
\draw[red] (appex1) -- (appex2);
\node[mypyr,draw] at (0,0) {};
\foreach \Coord in {1,...,4}
{
  \draw[opacity=0.6]
   (base1.corner \Coord) -- (base1.corner \the\numexpr\Coord+4\relax);
}
\end{tikzpicture}

\end{document}

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