Example: Symmetries of the plane

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% Symmetries of the plane
% Author: Cristóbal Camarero Coterillo
\documentclass[a4paper, 12pt, landscape]{article}
\usepackage[utf8]{inputenc}
\usepackage{textcomp}
\usepackage{tikz}
\usetikzlibrary{shapes,calc,decorations.pathmorphing,decorations.fractals}
\usepackage[bookmarks=true]{hyperref}
%landscape tuning
\setlength{\oddsidemargin}{0in}     % default=0in
\setlength{\textwidth}{9in}     % default=9in
\setlength{\columnsep}{0.5in}       % default=10pt
\setlength{\columnseprule}{1pt}     % default=0pt (no line)
\setlength{\textheight}{5.85in}     % default=5.15in
\setlength{\topmargin}{-0.15in}     % default=0.20in
\setlength{\headsep}{0.25in}        % default=0.35in
\setlength{\parskip}{1.2ex}
\setlength{\parindent}{0mm}
%PDF Settings
\newcommand\titulo{Symmetries of the plane}
\newcommand\autor{\href{http://www.alumnos.unican.es/ccc66}
  {Cristóbal Camarero Coterillo}}
\hypersetup{
    %bookmarks=true,         % show bookmarks bar?
    unicode=false,          % non-Latin characters in Acrobats bookmarks
    pdftoolbar=true,        % show Acrobats toolbar?
    pdfmenubar=true,        % show Acrobats menu?
    pdffitwindow=true,      % page fit to window when opened
    pdftitle={\titulo},     % title
    pdfauthor={\autor},     % author
    pdfsubject={symmetries of the plane in tikz},   % subject of the document
    pdfnewwindow=true,      % links in new window
    pdfkeywords={plane,symmetry,orbifold},% list of keywords
    pdfpagemode=None,       % avoid auto open bookmarks
    colorlinks=false,       % false: boxed links; true: colored links
    linkcolor=red,          % color of internal links
    citecolor=green,        % color of links to bibliography
    filecolor=magenta,      % color of file links
    urlcolor=cyan           % color of external links
}
\begin{document}
\newsavebox{\piece}%A TeX box to store the base tile (or orbifold)
\clearpage
%*632
\phantomsection\addcontentsline{toc}{chapter}{*632}%Add to PDF bookmarks
\savebox{\piece}{%We create the base tile
\begin{tikzpicture}[overlay]
\node[star,draw=red!50!black,inner sep=1pt] at (0.7,0.3) {};
\node[red,anchor=base] at (0.55,0.05) {\tiny $*632$};
\draw[thin] (0,0) -- ++(0:1) -- ++(120:0.5) --cycle;
\end{tikzpicture}}
\begin{center}%We replicate the tile according to the symmetry
\begin{tikzpicture}[every node/.style={anchor=center,draw=none}]
%The \i loop creates a supertile which can tile by translations
%which is done by the \a and \b loops
    \foreach \a in {0,...,7}
    \foreach \b in {0,...,7}
    \foreach \i in {0,1,2,3,4,5}
    {
        \path (0,0)
            ++(0:\a) ++(60:\a) ++(0:\b) ++(-60:\b)
            node[rotate=\i*60] {\usebox{\piece}}
            node[rotate=\i*60,yscale=-1] {\usebox{\piece}};
    }
\end{tikzpicture}
\end{center}
\clearpage
%632
\phantomsection\addcontentsline{toc}{chapter}{632}
\savebox{\piece}{%
\begin{tikzpicture}[overlay]
\node[blue] at (0.3,0.4) {\tiny 632};
\draw[thin] (0,0) -- ++(0:1) -- ++(120:1) --cycle;
\end{tikzpicture}}
\begin{center}
\begin{tikzpicture}[every node/.style={anchor=center,draw=none}]
    \foreach \a in {0,...,8}
    \foreach \b in {0,...,8}
    \foreach \i in {0,1,2,3,4,5}
    {
        \path (0,0)
            ++(0:\a) ++(60:\a) ++(0:\b) ++(-60:\b)
            node[rotate=\i*60] {\usebox{\piece}};
    }
\end{tikzpicture}
\end{center}
\clearpage
%*442
\phantomsection\addcontentsline{toc}{chapter}{*442}
\savebox{\piece}{%
\begin{tikzpicture}[overlay]
\node[arrow box,arrow box arrows={south:0.5cm,west:0.5cm},draw=red!50!black,inner sep=4pt] at (0.8,0.8) {};
\node[red,anchor=base] at (0.4,0.05) {\tiny $*442$};
\draw[thin] (0,0) -- ++(0:1) -- ++(90:1) --cycle;
\end{tikzpicture}}