Something like this:
`\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\begin{document}
\newcommand{\mk}{node [fill=black] {}}
\begin{tikzpicture}
\coordinate (O) at (0,0);
\foreach \x in {0,60,...,359}
{\draw (O) -- (\x:1);}
\foreach \x in {0,60,...,359}
{\draw (\x:1) -- +(\x+30:1);}
\foreach \x in {0,60,...,359}
{\draw (\x:1) -- +(\x-30:1);}
\foreach \x in {0,60,...,359}
{\draw (\x:1)++(\x+30:1) -- +(\x:1);}
\foreach \x in {0,60,...,359}
{\draw (\x:1)++(\x-30:1) -- +(\x:1);}
\foreach \x in {0,60,...,359}