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如何画二十面体？

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如何画二十面体？

在经历了pgf manual并且还在网上搜索一些解决方案或者至少是关于如何做到这一点的提示（最好使用 TikZ），所以我带着我的问题来到这里：

如何画二十面体？

我的想法是这样的：

二十面体

答案1

\documentclass{article}
\usepackage{pst-platon}
\pagestyle{empty}
\def\Gobble#1{}

\begin{document}
\psIcosahedron
\psIcosahedron[Frame=false,Viewpoint=-1 0.5 1.2,faceName=\arabic]
\psIcosahedron[Frame=false,faceName=\Gobble]
\end{document}

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答案2

问题关于多面体Herbert 给出了答案，它使用了pst-solides3d。它可以轻松扩展到当前的情况，只需替换octahedron为icosahedron：

%% Code by Herbert --> https://tex.stackexchange.com/a/17208/11232
\documentclass{article}
\usepackage[dvipsnames]{pstricks}
\usepackage{pst-solides3d}
\begin{document}

\begin{pspicture}(-2.5,-2)(2.5,2.5)
\psset{lightsrc=10 20 30,viewpoint=30 10 30 rtp2xyz,Decran=40}
 \psSolid[object=icosahedron,a=3,linecolor=blue,
          opacity=0.6,hollow,hue=0 1,
          action=draw**]
 \axesIIID(3,3,3)(6,4,4)
\end{pspicture}

\end{document}

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您必须使用xelatex或来编译它latex->dvips->ps2pdf。

答案3

您可以使用\usepackage{tikz,tikz-3dplot}

\documentclass[border=2 mm,12pt,tikz]{standalone}
\usepackage{tikz,tikz-3dplot} 
\usepackage{fouriernc}
\begin{document}
    \tdplotsetmaincoords{60}{100}
    \begin{tikzpicture}[tdplot_main_coords,scale=1,line join=round]
    \pgfmathsetmacro\a{2}
    \pgfmathsetmacro{\phi}{\a*(1+sqrt(5))/2}
    \path 
    coordinate(A) at (0,\phi,\a)
    coordinate(B) at (0,\phi,-\a)
    coordinate(C) at (0,-\phi,\a)
    coordinate(D) at (0,-\phi,-\a)
    coordinate(E) at (\a,0,\phi)
    coordinate(F) at (\a,0,-\phi)
    coordinate(G) at (-\a,0,\phi)
    coordinate(H) at (-\a,0,-\phi)
    coordinate(I) at (\phi,\a,0)
    coordinate(J) at (\phi,-\a,0)
    coordinate(K) at (-\phi,\a,0)
    coordinate(L) at (-\phi,-\a,0); 
    \draw[dashed, thick]    (B) -- (H) -- (F) 
    (D) -- (L) -- (H) --cycle 
    (K) -- (L) -- (H) --cycle
    (K) -- (L) -- (G) --cycle
    (C) -- (L) (B)--(K) (A)--(K)
    ;
        
        \draw[ultra thick]
        (A) -- (I) -- (B) --cycle 
        (F) -- (I) -- (B) --cycle 
        (F) -- (I) -- (J) --cycle
        (F) -- (D) -- (J) --cycle
        (C) -- (D) -- (J) --cycle
        (C) -- (E) -- (J) --cycle
        (I) -- (E) -- (J) --cycle
        (I) -- (E) -- (A) --cycle
        (G) -- (E) -- (A) --cycle
        (G) -- (E) -- (C) --cycle
        ; 
 %\foreach \point/\position in {A/right,B/below,C/above,D/left,E/{above right},F/below,G/above,H/left,I/below,J/right,K/below,L/left}
%{
    %\fill (\point) circle (1.5pt);
    %\node[\position=3pt] at (\point) {$\point$};
%}

\end{tikzpicture}
\end{document}

您可以使用3dtools 这里画出这个。

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{backgrounds,3dtools}
\begin{document}
        \pgfdeclarelayer{background} 
    \pgfdeclarelayer{foreground}
    \pgfsetlayers{background,main,foreground}
    \begin{tikzpicture}[scale=2,line cap=round,line join=round]
    \edef\lstV{{0., 0., -0.951057}, {0., 0., 0.951057}, {-0.850651, 0., -0.425325}, {0.850651, 0., 0.425325}, {0.688191, -0.5, -0.425325}, {0.688191, 0.5, -0.425325}, {-0.688191, -0.5, 0.425325}, {-0.688191, 0.5, 0.425325}, {-0.262866, -0.809017, -0.425325}, {-0.262866, 0.809017, -0.425325}, {0.262866, -0.809017, 0.425325}, {0.262866, 0.809017, 0.425325}}
    \edef\lstFaces{{2,12,8},{2,8,7},{2,7,11},{2,11,4},{2,4,12},{5,9,1},{6,5,1},{10,6,1},{3,10,1},{9,3,1},{12,10,8},{8,3,7},{7,9,11},{11,5,4},{4,6,12},{5,11,9},{6,4,5},{10,12,6},{3,8,10},{9,7,3}}
    \tikzset{3d/polyhedron/.cd,fore layer=foreground,back layer=background, 
        fore/.append style={fill opacity=0.7},back/.append style={fill opacity=0.7}}
    \begin{scope}[3d/install view={phi=120,psi=20,%
            theta=70}]
        \tikzset{name prefix=Va,%<- used for all vertices
            3d/define vertices/.expanded={\lstV},
            3d/polyhedron/create faces from vertex list/.expanded={\lstFaces}}
         \pgfmathtruncatemacro{\mydim}{dim({\lstV})} % number of vertices
        \foreach \X in {1,...,\mydim}
        {\edef\p{\pgfkeysvalueof{/tikz/name prefix}\X}
            \pgfmathsetmacro{\myp}{TD("(\p)")}
            \pgfmathtruncatemacro{\mysd}{sign(screendepth(\myp))}
            \ifnum\mysd<0
            \draw[fill=black,on layer=background] (\p) %node[above,scale=0.3]{$\p$} 
            circle[radius=0.6 pt];
            \else
            \draw[fill=black,on layer=foreground] (\p) %node[above,scale=0.3]{$\p$} 
            circle[radius=0.6 pt];
            \fi}
    \end{scope}
    \end{tikzpicture}
\end{document}

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