Hexagonal diagrams

Question

I would like to draw a hexagonal diagram made up of many small equilateral triangles, and be able to label specific vertices in the diagram. In particular, something like this:

But ideally rotated so that one of the sides is on top rather than a vertex.

Could someone point me in the right direction?

Answer 1

I try to find another way in the spirit of TikZ without complicated macros.

First part : the method

First I define vertices. Some of them are on circle and define hexagons. Circles or hexagons are numeroted from 0 to 3. 0 is the center. Then on each hexagons, I place vertices numeroted from 0 to 5 for the first; 0 to 11 for the second and 0 to 17 for the third one. In a first time,I use nodes but for the final drawing, I will use coordinates. A vertice is defined by h;i h for hexagon and i for indice.

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{calc,arrows}

\begin{document}
\begin{tikzpicture}
  %%%  define vertices with coordinates     
\node (00) at (0,0) {00}; 
\foreach \c in {1,...,3}{%  
\foreach \i in {0,...,5}{% 
\pgfmathtruncatemacro\j{\c*\i}
 % little trick \c*\i  gives 0,1,2,3,4,5 for this first circle
 % 0,2,4 etc.. for the second one and 0,3,6 for the third one.
 % the for the second hexagon, i define the midpoints ith indices : 1,3,5,..
 % and for the third hexagon , two points betweens 3;0 and 3;3 etc...

 %  pgfmathtruncatemacro is used because we can't accept 3;2.0 for a name
\node[circle,minimum width=4pt,inner sep=0pt] (\c;\j) at (60*\i:\c){\c;\j};  
} }
% now on the second hexagon we need to place between each corners, a midpoint
% to finish we need to change 12 in 0 so I use  mod 
\foreach \i in {0,2,...,10}{%
 % perhaps foreach now gives some possibilities to avoid  \pgfmathtruncatemacro
\pgfmathtruncatemacro\j{mod(\i+2,12)}% 
\pgfmathtruncatemacro\k{\i+1}
 % midpoint I use the same method further 
\node (2\k) at ($(2;\i)!.5!(2;\j)$)  {2;\k} ;    }

% now on the third hexagon we need to place between each corners, two points
% to finish we need to change 18 in 0 so I use  mod
%  ($(3;\i)!1/3!(3;\j)$) is a barycenter coeff 1 and 2
\foreach \i in {0,3,...,15}{% 
\pgfmathtruncatemacro\j{mod(\i+3,18)} 
\pgfmathtruncatemacro\k{\i+1} 
\pgfmathtruncatemacro\l{\i+2}
\node (3\k) at ($(3;\i)!1/3!(3;\j)$)  {3;\k} ;
\node (3\l) at ($(3;\i)!2/3!(3;\j)$)  {3;\l} ;
 }     
\end{tikzpicture} 
\end{document}

I get this picture. You can see the names of the nodes.

Second part : Drawing the graph

I change node with coordinates

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{calc,arrows}


\begin{document}

\begin{tikzpicture}
%%%  define vertices with coordinates
\coordinate (0;0) at (0,0); 
\foreach \c in {1,...,3}{%  
\foreach \i in {0,...,5}{% 
\pgfmathtruncatemacro\j{\c*\i}
\coordinate (\c;\j) at (60*\i:\c);  
} }
\foreach \i in {0,2,...,10}{% 
\pgfmathtruncatemacro\j{mod(\i+2,12)} 
\pgfmathtruncatemacro\k{\i+1}
\coordinate (2;\k) at ($(2;\i)!.5!(2;\j)$) ;}

\foreach \i in {0,3,...,15}{% 
\pgfmathtruncatemacro\j{mod(\i+3,18)} 
\pgfmathtruncatemacro\k{\i+1} 
\pgfmathtruncatemacro\l{\i+2}
\coordinate (3;\k) at ($(3;\i)!1/3!(3;\j)$)  ;
\coordinate (3;\l) at ($(3;\i)!2/3!(3;\j)$)  ;
 }

 %%%%%%%%% draw lines %%%%%%%%
 \foreach \i in {0,...,6}{% 
 \pgfmathtruncatemacro\k{\i}
 \pgfmathtruncatemacro\l{15-\i}
 \draw[thin,gray] (3;\k)--(3;\l);
 \pgfmathtruncatemacro\k{9-\i} 
 \pgfmathtruncatemacro\l{mod(12+\i,18)}   
 \draw[thin,gray] (3;\k)--(3;\l); 
 \pgfmathtruncatemacro\k{12-\i} 
 \pgfmathtruncatemacro\l{mod(15+\i,18)}   
 \draw[thin,gray] (3;\k)--(3;\l);}    
%%%%%%%%% some specific lines %%%%%%%%%% 
 \foreach \i in {0,2,...,10} {
   \pgfmathtruncatemacro\j{mod(\i+2,12)} 
   \draw[thick,dashed] (2;\i)--(2;\j);}     
%%%%%%%%% draw points %%%%%%%% 
\fill [gray] (0;0) circle (2pt);
 \foreach \c in {1,...,3}{%
 \pgfmathtruncatemacro\k{\c*6-1}    
 \foreach \i in {0,...,\k}{% 
   \fill [gray] (\c;\i) circle (2pt);}}  
%%%%%%%%% some specific points %%%%%%%%%%  
 \foreach \n in {0,3,...,15}{% 
   \draw (3;\n) circle (4pt);}
 \foreach \n in {1,3,...,11}{% 
   \draw (2;\n) circle (4pt);}
%%%%%%%%%% arrows %%%%%%%%%%%%
\draw[->,red,thick,shorten >=4pt,shorten <=2pt](0;0)--(2;3);
\draw[->,red,thick,shorten >=4pt,shorten <=2pt](0;0)--(2;1); 
\end{tikzpicture}  
\end{document}

The result :

Answer 2

Sorry it's not a good example of code with tkz-berge but there are a lot of possibilities with tkz-graph and tkz-berge that I made the most simple without great ideas.

You need to find better names. To see the names of vertices you can change Art with Classic \GraphInit[vstyle=Classic]

\documentclass[]{article}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{tkz-berge}
\begin{document}

\begin{tikzpicture}
\GraphInit[vstyle=Art]
   \SetGraphUnit{2} 
   \Vertex{A}     
   \grCycle[prefix=a,rotation=30,RA=6]{6}
   {\SetUpEdge[style={ultra thick},color=red]
   \grCycle[prefix=b,RA=3.464]{6} } 
   \SetVertexArt[MinSize    = 4pt]  
   \grCycle[prefix=c,rotation=30,RA=2]{6}     
   \grCycle[prefix=d,rotation=30,RA=4]{6}
   \NO(d2){e2} \NO(b2){e3} 
   \NO(b1){e4} \NO(d0){e5}
   \SO(d3){e6} \SO(b4){e7} 
   \SO(b5){e8} \SO(d5){e9}
   \NO(a3){f1} \NO(f1){f2} 
   \NO(a5){f3} \NO(f3){f4}
   \Edges(a2,d2,c2,A,c5,d5,a5)
   \Edges(a3,d3,c3,A,c0,d0,a0) 
   \Edges(a4,d4,c4,A,c1,d1,a1)
   \Edges(f2,d2,e2,b2,c1,b1,e4,d1) 
   \Edges(d1,e3,b2,c2,b3,f1) 
   \Edges(d0,f4,b0,c5,b5,e8,d4,e7,b4,c3,b3,f2) 
   \Edges(d0,e5,b1,c0,b0,f3,d5,e9,b5,c4,b4,e6,d3,f1)
   \SetUpEdge[style={->,ultra thick,double},color=blue]
   \Edges(A,b0)  \Edges(A,b1)
 \end{tikzpicture}   
\end{document}

I forgot the rotation :

\begin{tikzpicture}[rotate=30] ....

A better idea to begin this code is :

 \begin{tikzpicture}
\GraphInit[vstyle=Art]
 \SetVertexArt[MinSize  = 4pt] 
   \SetGraphUnit{2}
     \grCycle[prefix=V,RA=4]{6}
     \foreach \n in {0,...,5}{%
     \begin{scope}[shift=(V\n)]
        \grCycle[prefix=V\n,RA=2]{6}
     \end{scope}}   
 \end{tikzpicture}

version 3

 \begin{tikzpicture}
   \foreach \n in {0,...,3} 
    {\begin{scope}[shift={({\n*sqrt(3)},\n)},rotate=90]
    \pgfmathsetmacro\order{7-\n} 
    \grEmptyPath[prefix=\n,RA=2]{\order} 
 \end{scope} } 
    \foreach \n in {-1,...,-3} 
    {  \begin{scope}[shift={({\n*sqrt(3)},-\n)},rotate=90]
    \pgfmathsetmacro\order{7+\n} 
 \grEmptyPath[prefix=\n,RA=2]{\order} 
 \end{scope} } 
 \end{tikzpicture} 

Answer 3

Download geogebra and draw the figure. You can then export it as a TikZ or PSTricks and use it within LaTeX.

Answer 4

I suggest you my solution. It is a little bit tricky and probably it is not the most beautiful TikZ/TeX code around the web, but it works fine and it is identical to original picture.

EDIT: just cleaned up a bit the code

Here we go the code:

\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{calc,intersections,arrows}


\begin{document}

%%%%%%%% INPUT %%%%%%%
\def\edge{1.2}       %
\def\N{4}            %
\def\LabelsOn{0}     %
\def\IntRadius{0.05} %
\def\ExtRadius{0.08} %
%%%%%%%%%%%%%%%%%%%%%%
\pgfdeclarelayer{background}
\pgfsetlayers{background,main}
\begin{tikzpicture}[>         = latex,
                    shorten > = \IntRadius cm,
                    shorten < = \IntRadius cm]

\pgfmathtruncatemacro{\cond}{mod(\N,2)}
\pgfmathtruncatemacro{\condI}{mod(\N,3)}
\pgfmathsetmacro{\cosine}{cos(30)}

\def\ClipOn#1{
\foreach[count=\t] \ang in {0,60,...,360}{
\coordinate (P\t) at (\ang:#1);
}
\clip (P1)--(P2)--(P3)--(P4)--(P5)--(P6)--cycle;
}


\ifnum\cond=0%pari
  \gdef\cond{0}
\else
  \gdef\cond{1}
\fi
\ClipOn{\N*\edge+\ExtRadius/\cosine+0.02}
\foreach[count=\t] \row in {-\N,...,\N}{
   \ifnum\cond=0
     \def\translate{0}
   \else
     \def\translate{\edge/2}
   \fi
   \ifnum\condI=0 %divisibile per 3
     \gdef\circles{3}
   \else
     \pgfmathtruncatemacro{\temp}{\condI-1}
     \global\let\circles\temp
   \fi
   \begin{pgfonlayer}{background}
   \ClipOn{\N*\edge}
   \draw[lightgray] (-\N*\edge,\row*\edge*\cosine)--++(2*\N*\edge,0);
   \end{pgfonlayer}
   \foreach \column in {-\N,...,\N}{
     \coordinate (\row/\column) at (\column*\edge+\translate,\row*\edge*\cosine);
     \ifnum0=\row
       \begin{pgfonlayer}{background}
       \ClipOn{\N*\edge}
       \foreach \deltaAng in {60,120}{
       \draw[lightgray] ($(\row/\column)+(180+\deltaAng:\N*\edge)$)--
                        ($(\row/\column)+(\deltaAng:\N*\edge)$);
       }
       \end{pgfonlayer}
     \fi
     \ifnum\LabelsOn=1
       \node[above] at (\row/\column){\row/\column};
     \fi
     \fill (\row/\column)circle[radius=\IntRadius];
     \ifnum\circles=3
       \ifnum\cond=0
         \draw (\row/\column)circle[radius=\ExtRadius];
       \else
         \draw ($(\row/\column)+(-2*\edge,0)$)circle[radius=\ExtRadius];
       \fi
       \pgfmathtruncatemacro{\temp}{\circles-2}
     \else
       \pgfmathtruncatemacro{\temp}{\circles+1}
     \fi
     \global\let\circles\temp
   }
   \ifnum\cond=0
    \gdef\cond{1}
   \else
    \gdef\cond{0}
   \fi
}
\draw[line width=1pt] (P1)--(P2)--(P3)--(P4)--(P5)--(P6)--cycle;

\draw[dashed,line width=1pt] (2/1)--(2/-1)--(0/-2)--(-2/-1)--(-2/1)--(0/2)--cycle;

\draw[->,red,line width=1.1pt](0/0)--(1/1)--(0/2);
\draw[->,red,line width=1.1pt](0/0)--(2/0);

\end{tikzpicture}
\end{document}

The result is the following:

The input are:

1. \edge = triangle edge length
2. \N = number of node on the radius less the center one
3. \LabelsOn = if setted to 1, it shows all the node name. It is useful to draw the arrows and the hexagons. See the picture below for what I mean.

I could add the circle radius input and so on.

If someone has some idea to improve the code, you are welcome.

Hope it helps.

Azoun