Tutte's 8-cage

The unique smallest cubic graph of girth 8. Drawn from Algebraic Graph Theory by Godsil and Royle, p.72.

\documentclass{article}
\usepackage{tikz}
\pagestyle{empty}

\begin{document}
\begin{tikzpicture}[style=thick]
\foreach \x in {0,36,...,324}
{
\draw (\x:2cm) circle (2pt) -- (\x+144:2cm);
\draw (\x-10:3cm) circle (2pt) -- (\x+5:4cm);
\draw (\x-10:3cm) circle (2pt) -- (\x+36:2cm);
\draw (\x-10:3cm) circle (2pt) -- (\x+170:3cm);
\draw (\x+5:4cm) circle (2pt) -- (\x+41:4cm);
}
\end{tikzpicture}
\end{document}