19

After going through the pgf manual and also searching the web for some solution or at least a hint on how it can be done (preferably using TikZ), so I came here with my question:

How to draw an Icosahedron?

This is what I have in mind:

Icosahedron

rtzll
  • 5,531
  • 4
    You can see at http://tex.stackexchange.com/questions/17204/drawing-polyhedra-using-tikz-with-semi-transparent-and-shading-effect – minthao_2011 Dec 31 '12 at 14:42
  • 1
    See also: 3d axis and polyhedron with line segment towards origin – Claudio Fiandrino Dec 31 '12 at 14:50
  • 2
    You can find the coordinates of the vertices here: http://en.wikipedia.org/wiki/Icosahedron#Cartesian_coordinates – Ethan Bolker Dec 31 '12 at 15:13
  • 2
    Quoting @AndrewStacey from http://tex.stackexchange.com/questions/4701/drawing-3d-diagrams: whilst I agree that TikZ has some severe limitations for drawing 3D pictures, calculating the projections by hand is not one of them. You can specify coordinates in 3D and draw some very obviously 3D pictures - take a look at my contributions on texample.net to see some, or look at the "how to draw a torus" question on this site. – Andrew Stacey Oct 30 '10 at 11:05 – Ethan Bolker Dec 31 '12 at 15:38

3 Answers3

28
\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}

enter image description here

15

The question on polyhedra has an answer by Herbert and it uses pst-solides3d. It can be easily extended for the present case by just replacing octahedron by 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}

enter image description here

You have to compile this with xelatex or latex->dvips->ps2pdf.

Community
  • 1
13

You can use \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}

You can use 3dtools here to draw this.

\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}

enter image description here

enter image description here

minhthien_2016
  • 9,467