How to draw an Icosahedron?

\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}

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}

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

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}