\documentclass{standalone}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,mindmap,shapes,positioning,snakes,calc}
\tikzset{
tag/.style={
rectangle,
draw=black, very thick,
text width=4em,
minimum height=2em,
text centered},
commit/.style={
circle,
draw=black, very thick,
text width=1em,
minimum height=1em,
text centered},
point/.style={coordinate},
}
\pgfplotsset{compat=1.6}
\begin{document}
\def \phi {1.617}
\begin{tikzpicture}[
x={(-0.86in, -0.5in)}, y = {(0.86in, -0.5in)}, z = {(0, 1in)},
rotate = 22,
scale = 0.6,
every node/.style = {
circle, fill = blue!20, inner sep = 0pt, minimum size = 0.5cm
},
foreground/.style = { ultra thick },
background/.style = { dashed }
]
\coordinate (9) at (0, -\phi*\phi, \phi);
\coordinate (8) at (0, \phi*\phi, \phi);
\coordinate (12) at (0, \phi*\phi, -\phi);
\coordinate (5) at (0, -\phi*\phi, -\phi);
\coordinate (7) at ( \phi, 0, \phi*\phi);
\coordinate (3) at (-\phi, 0, \phi*\phi);
\coordinate (6) at (-\phi, 0, -\phi*\phi);
\coordinate (4) at ( \phi, 0, -\phi*\phi);
\coordinate (2) at ( \phi*\phi, \phi, 0);
\coordinate (10) at (-\phi*\phi, \phi, 0);
\coordinate (1) at (-\phi*\phi, -\phi, 0);
\coordinate (11) at ( \phi*\phi, -\phi, 0);
\draw[foreground] (10) -- (3) -- (8) -- (10) -- (12) -- (8);
\draw[foreground] (4) -- (12) -- (2) -- (4) -- (11) -- (2);
\draw[foreground] (9) -- (3) -- (7) -- (9) -- (11) -- (7);
\draw[foreground] (7) -- (8) -- (2) -- cycle;
\draw[background] (12) -- (6) -- (10) -- (1) -- (6) -- (5) -- (1)
-- (9) -- (5) -- (11);
\draw[background] (5) -- (4) -- (6);
\draw[background] (3) -- (1);
\foreach \n in {1,...,12}
\node at (\n) {\n};
\end{tikzpicture}
\end{document}