Truncated Icosahedron in TikZ?

Let's start with the skeleton. Coordinates are copy from polyhedron_js.asy.

\documentclass[border=9,tikz]{standalone}

\usepackage{tikz-3dplot}

\begin{document}
\foreach\s in{2,4,...,360}{
    \tdplotsetmaincoords{2.71828+\s}{2.71828+\s*2}
    \tikz[tdplot_main_coords,scale=.1]{
        \path(-150cm,-150cm)(150cm,150cm);
        \draw
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    }
}

\end{document}