\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}