# Drawing hexagons

I have a case where I need to draw a hexagonal grid in LaTeX. I am considering just reading the grid from an eps file.

Is there an alternative way to do it completely within LaTeX?

• You can use TikZ and adopt the code from this triangular grid. Nov 26 '10 at 23:14
• as usual tikz or pstricks or metapost among others Nov 26 '10 at 23:17
• By the way, I was quite amused by your no-so-veiled "threat" to LaTeX: "I am considering just reading the grid from an eps file.".... :-) Nov 28 '10 at 9:18
• Thanks for mentioning TikZ. I want to typeset some astrology charts and this might be just the thing. Nov 28 '10 at 23:14

Here's a quick option:

\begin{tikzpicture}
\foreach \i in {0,...,3}
\foreach \j in {0,...,3} {
\foreach \a in {0,120,-120} \draw (3*\i,2*sin{60}*\j) -- +(\a:1);
\foreach \a in {0,120,-120} \draw (3*\i+3*cos{60},2*sin{60}*\j+sin{60}) -- +(\a:1);}
\end{tikzpicture}


Which results in

• That is an amazingly good solution! Nov 27 '10 at 12:48
• I have to give you the checkmark. You did exactly how I dreamt it. Nov 29 '10 at 0:13
• Took a bit of searching for the code to do this (but faster than doing it myself) but thanks. It's helped me too. Apr 8 '13 at 23:09
• I would like to number your hexagons following an order that I set. It's possible to do this? Nov 11 '15 at 21:58
• How to set the hexagons larger?
– bmv
Mar 18 '18 at 20:18

With TikZ, you can define a pattern which allows to fill any shape with a hexagonal grid by adding the option pattern=hexagons:

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{patterns}

\def\hexagonsize{0.5cm}
\pgfdeclarepatternformonly
{hexagons}% name
{\pgfpointorigin}% lower left
{\pgfpoint{3*\hexagonsize}{0.866025*2*\hexagonsize}}%  upper right
{\pgfpoint{3*\hexagonsize}{0.866025*2*\hexagonsize}}%  tile size
{% shape description
\pgfsetlinewidth{0.4pt}
\pgftransformshift{\pgfpoint{0mm}{0.866025*\hexagonsize}}
\pgfpathmoveto{\pgfpoint{0mm}{0mm}}
\pgfpathlineto{\pgfpoint{0.5*\hexagonsize}{0mm}}
\pgfpathlineto{\pgfpoint{\hexagonsize}{-0.866025*\hexagonsize}}
\pgfpathlineto{\pgfpoint{2*\hexagonsize}{-0.866025*\hexagonsize}}
\pgfpathlineto{\pgfpoint{2.5*\hexagonsize}{0mm}}
\pgfpathlineto{\pgfpoint{3*\hexagonsize+0.2mm}{0mm}}
\pgfpathmoveto{\pgfpoint{0.5*\hexagonsize}{0mm}}
\pgfpathlineto{\pgfpoint{\hexagonsize}{0.866025*\hexagonsize}}
\pgfpathlineto{\pgfpoint{2*\hexagonsize}{0.866025*\hexagonsize}}
\pgfpathlineto{\pgfpoint{2.5*\hexagonsize}{0mm}}
\pgfusepath{stroke}
}
\begin{document}

\begin{tikzpicture}
\fill[pattern=hexagons] (0,0) rectangle (10,5);
\end{tikzpicture}

\begin{tikzpicture}
\fill[pattern=hexagons] (0,0) circle (3cm);
\end{tikzpicture}

\end{document}


You can change the size of the hexagons by modifying the value of the macro \hexagonsize.

• I like it! Nice solution. Nov 29 '10 at 8:16
• Ah finally found it. I was looking for this nice snippet for a while with bad keywords :-) Would you like to write an answer to the open question tex.stackexchange.com/questions/54358/… ? I think this would be the perfect example. Jun 17 '12 at 21:32
• @percusse: thanks for notifying me. I'll add an answer later on. Jun 18 '12 at 6:34

Another way could be to draw hexagonal nodes over an adjusted coordinate system. The idea came adapting Paul Gaborit's Pascal triangle for How can I draw Pascal's triangle with some its properties?.

shapes.geometric library helps to draw hexagon where the minimum size is the diameter of the circumcircle. Therefore, selecting adjusted values for x (x=1.5*{minimum size}) and y (y=\sqrt{.75}*{minimum size}/2) the hexagonal grid can be drawn placing an node centered in every pair (x,y).

\documentclass[border=2mm, tikz]{standalone}
\usetikzlibrary{shapes.geometric}
\begin{document}

%
% x=3*(minimum size)/2
% x=\sqrt{3/4}*(minimum size)/2
%
\begin{tikzpicture}[x=7.5mm,y=4.34mm]
% some styles
\tikzset{
box/.style={
regular polygon,
regular polygon sides=6,
minimum size=10mm,
inner sep=0mm,
outer sep=0mm,
rotate=0,
draw
}
}

\foreach \i in {0,...,5}
\foreach \j in {0,...,5} {
\node[box] at (2*\i,2*\j) {};
\node[box] at (2*\i+1,2*\j+1) {};
}

\end{tikzpicture}

\end{document}


• What are the [x=7.5mm,y=4.34mm] parameters for the Tikz package? Jan 6 '16 at 1:13
• @jvriesem They define base vectors for the coordinate system. By default,x=1cm and y=1cm. When you say (2,3), TiKZ reads (2*x,3*y). Better explanation can be found in Coordiante system in TiKZ documentation. Jan 6 '16 at 21:11
• @Ignasi How to set the hexagons larger?
– bmv
Mar 18 '18 at 20:18
• @bmv Change minimum size and values of x and y accordingly Mar 18 '18 at 21:31

And a Metapost approach...

prologues := 3;
outputtemplate := "%j%c.eps";

beginfig(1);

% r = side of hexagon, n = repetitions of the grid (- and +)
r = 5mm; n=10;

% make a shape to draw
path tri; tri = for t=0 step 120 until 359: origin -- (r,0) rotated t -- endfor cycle;

% save the pattern as a picture centered on the origin
picture grid; grid = image(
for i=-n upto n:
for j=-n upto n:
draw tri shifted (i*3/2r,j*r*sqrt(3)) if (i mod 2)=1: shifted (0,r/2*sqrt(3)) fi ;
endfor
endfor);

% clip the pattern as required (to get rid of the rough edges...)
clip grid to fullcircle scaled (2*n*r);

% draw as needed
draw grid;
draw grid rotated 30 shifted (2n*r,0) withcolor .67 red;

endfig;
end.

  \documentclass[tikz,border=5mm]{standalone}
\usetikzlibrary{calc,patterns}
\newlength{\dodamnet}
\newcommand{\bankinh}{}
\newcommand{\maumot}{}
\newcommand{\mauhai}{}
\newcommand{\mauba}{}
\newcommand{\maubon}{}
\tikzset{
do dam net/.code={\setlength{\dodamnet}{#1}},
ban kinh/.code={\renewcommand{\bankinh}{#1}},
mau mot/.code={\renewcommand{\maumot}{#1}},
mau hai/.code={\renewcommand{\mauhai}{#1}},
mau ba/.code={\renewcommand{\mauba}{#1}},
mau bon/.code={\renewcommand{\maubon}{#1}}
}
\tikzset{
do dam net=0.5pt,
mau mot=red,
mau hai=blue,
mau ba=pink,
mau bon=yellow,
ban kinh =1
}
\begin{document}
\pgfdeclarepatternformonly[\bankinh,\maumot,\mauhai,\mauba,\maubon,\dodamnet]{luc giac mau}
{\pgfmathsetmacro{\x}{1.5* \bankinh}
\pgfmathsetmacro{\y}{\bankinh *sqrt(3)}
\pgfqpoint{-\x mm}{-\y mm}}%Dưới trái
{\pgfmathsetmacro{\x}{1.5* \bankinh}
\pgfmathsetmacro{\y}{\bankinh *sqrt(3)}
\pgfqpoint{\x mm}{\y mm}}%Trên phải
{\pgfmathsetmacro{\x}{3* \bankinh}
\pgfmathsetmacro{\y}{2*\bankinh *sqrt(3)}
\pgfqpoint{\x mm}{\y mm}}
%======================
{\pgfsetlinewidth{\dodamnet}
\pgfmathsetmacro{\nuabk}{\bankinh/2}
\pgfmathsetmacro{\cao}{\nuabk *sqrt(3)}
\pgfmathsetmacro{\y}{2*\cao}
\pgfmathsetmacro{\x}{1.5* \bankinh}
\pgfsetfillcolor{\maumot}
\pgfpathmoveto{\pgfqpoint{-\nuabk mm}{-\cao mm}}
\pgfpathlineto{\pgfqpoint{-\bankinh mm}{0 mm}}
\pgfpathlineto{\pgfqpoint{-\nuabk mm}{\cao mm}}
\pgfpathlineto{\pgfqpoint{\nuabk mm}{\cao mm}}
\pgfpathlineto{\pgfqpoint{\bankinh mm}{0 mm}}
\pgfpathlineto{\pgfqpoint{\nuabk mm}{-\cao mm}}
\pgfpathlineto{\pgfqpoint{-\nuabk mm}{-\cao mm}}
\pgfusepath{fill}
\pgfsetfillcolor{\mauhai}
\pgfpathmoveto{\pgfqpoint{-\x mm}{-\y mm}}
\pgfpathlineto{\pgfqpoint{-\bankinh mm}{-\y mm}}
\pgfpathlineto{\pgfqpoint{-\nuabk mm}{-\cao mm}}
\pgfpathlineto{\pgfqpoint{-\bankinh mm}{0 mm}}
\pgfpathlineto{\pgfqpoint{-\x mm}{0 mm}}
\pgfpathmoveto{\pgfqpoint{\x mm}{-\y mm}}
\pgfpathlineto{\pgfqpoint{\bankinh mm}{-\y mm}}
\pgfpathlineto{\pgfqpoint{\nuabk mm}{-\cao mm}}
\pgfpathlineto{\pgfqpoint{\bankinh mm}{0 mm}}
\pgfpathlineto{\pgfqpoint{\x mm}{0 mm}}
\pgfusepath{fill}
\pgfsetfillcolor{\mauba}
\pgfpathmoveto{\pgfqpoint{-\x mm}{\y mm}}
\pgfpathlineto{\pgfqpoint{-\bankinh mm}{\y mm}}
\pgfpathlineto{\pgfqpoint{-\nuabk mm}{\cao mm}}
\pgfpathlineto{\pgfqpoint{-\bankinh mm}{0 mm}}
\pgfpathlineto{\pgfqpoint{-\x mm}{0 mm}}
\pgfpathmoveto{\pgfqpoint{\x mm}{\y mm}}
\pgfpathlineto{\pgfqpoint{\bankinh mm}{\y mm}}
\pgfpathlineto{\pgfqpoint{\nuabk mm}{\cao mm}}
\pgfpathlineto{\pgfqpoint{\bankinh mm}{0 mm}}
\pgfpathlineto{\pgfqpoint{\x mm}{0 mm}}
\pgfusepath{fill}
\pgfsetfillcolor{\maubon}
\pgfpathmoveto{\pgfqpoint{-\bankinh mm}{\y mm}}
\pgfpathlineto{\pgfqpoint{-\nuabk mm}{\cao mm}}
\pgfpathlineto{\pgfqpoint{\nuabk mm}{\cao mm}}
\pgfpathlineto{\pgfqpoint{\bankinh mm}{\y mm}}
\pgfpathmoveto{\pgfqpoint{-\bankinh mm}{-\y mm}}
\pgfpathlineto{\pgfqpoint{-\nuabk mm}{-\cao mm}}
\pgfpathlineto{\pgfqpoint{\nuabk mm}{-\cao mm}}
\pgfpathlineto{\pgfqpoint{\bankinh mm}{-\y mm}}
\pgfusepath{fill}
}
\begin{tikzpicture}
\draw[pattern=luc giac mau] (0,0) rectangle (4,1);
\draw[pattern=luc giac mau,mau mot=gray,mau hai=purple,mau ba=orange,mau bon=pink] (0,2) rectangle (4,3);
\end{tikzpicture}
\end{document}


• Hi, welcome. Your code is not compileable. Oct 26 '19 at 17:59
• Thanks! This is my first post Oct 26 '19 at 18:03