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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

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You can see at tex.stackexchange.com/questions/17204/… –  minthao_2011 Dec 31 '12 at 14:42
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You can find the coordinates of the vertices here: en.wikipedia.org/wiki/Icosahedron#Cartesian_coordinates –  Ethan Bolker Dec 31 '12 at 15:13
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Quoting @AndrewStacey from 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
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2 Answers 2

up vote 16 down vote accepted
\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

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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 --> http://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.

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