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\documentclass{standalone}
\usepackage{tikz}
\usepackage{graphene}
% rescale cells by
\def\rr{4}
\begin{document}
\begin{tikzpicture}
%\graphene{(0,0)}{12}{12}
\graphene{(-3,3*\sqrtTh)}{17}{16}
\foreach \i in {0,...,3}{
\draw[line width=1pt, color=blue](-1*\rr,-\i*\sqrtTh*\rr)--++(1.5*2*\i*\rr+3*\rr,\sqrtThOT*2*\i*\rr+\sqrtTh*\rr);
}
\foreach \i in {0,...,3}{
\draw[line width=1pt, color=blue](0.5*\rr+3*\i*\rr,-3.5*\sqrtTh*\rr)--++(-1.5*2*\i*\rr+12*\rr,-\sqrtThOT*2*\i*\rr+4*\sqrtTh*\rr);
}
\foreach \i in {0,...,3}{
\draw[line width=1pt, color=blue](-1*\rr,-\i*\sqrtTh*\rr)--++(-1.5*2*\i*\rr+10.5*\rr,+\sqrtThOT*2*\i*\rr-3.5*\sqrtTh*\rr);
}
\foreach \i in {0,...,3}{
\draw[line width=1pt, color=blue](-1*\rr+3*\i*\rr,\sqrtTh*\rr)--++(-1.5*2*\i*\rr+13.5*\rr,\sqrtThOT*2*\i*\rr-4.5*\sqrtTh*\rr);
}
\end{tikzpicture}
\end{document}
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