Ytukyg

I would like to draw a regual 21 polygon, where the edges are labelled and have arrows in the middle. But I don't know how to get the arrows.
This is what I have done so far

documentclass[border=5mm, tikz]{standalone}

usetikzlibrary{shapes.geometric}

begin{document}



begin{tikzpicture}



node (pol) [

  draw,

  minimum size=0.9textwidth,

  regular polygon, regular polygon sides=21,

  rotate=270,

  ]{};

foreach x/y/i in {1/2/1,3/4/1,5/6/2,7/8/2,9/10/3,11/12/3}

  path[auto=right]

    (pol.corner x)--(pol.corner y)

      node[midway]{$alpha_ {i}$};

foreach x/y/i in {2/3/1,4/5/1,6/7/2,8/9/2,10/11/3,12/13/3}

  path[auto=right]

    (pol.corner x)--(pol.corner y)

      node[midway]{$beta_ {i}$};

 foreach x/y/i in {13/14/1, 15/16/1, 16/17/2,18/19/2,19/20/3,21/1/3}

  path[auto=right]

    (pol.corner x)--(pol.corner y)

      node[midway]{$xi_ {i}$};

      foreach x/y/i in {14/15/1,17/18/2,20/21/3}

  path[auto=right]

    (pol.corner x)--(pol.corner y)

      node[midway]{$rho_ {i}$};

end{tikzpicture}



end{document}

This gives me

I would like to have something like this

How can I add these arrows? I would prefer to expand my existing code rather then using soomething completely different, unless I did it way too complicated?

Here is what I got using my personal style ->- and -<-. To make it more versatile, I also define several arrow types, try it out using say draw[->-=6pt red 2] (0,0) -- (1,1); where 6pt is the size of the arrow, red the color and 2 the type. One good thing about ->- and -<- is that the center of the arrow is perfectly at the middle of the path, and the direction of the arrow is exactly the same as the tangential direction at the middle point of the path (works for any path type, -- line, curve to lines etc), Here is an example illustrating this point.

documentclass[margin=0pt]{standalone}

usepackage[svgnames]{xcolor}

%---------------------------- Tikz Libraries ------------------------------%

usepackage{ifthen}

usepackage{tikz}

usetikzlibrary{shapes.geometric}

usetikzlibrary{decorations, decorations.markings} 



%==========================  Middle & pointing arrows ==========================%

%-------------------------------------------------------------------------------%

% usage: draw[->-] or draw[->-=6pt red 1]

%-------------------------------------------------------------------------------%

tikzset{

  ->-/.style args={#1 #2 #3}{

    decoration={

      markings,

      mark= at position 0.5 with

      {

        ifthenelse{#3 = 1}

        {

          fill[#2] (#1/-6.0,0pt) -- (-0.5*#1, #1/3.0) -- (0.5*#1,0pt) -- (-0.5*#1, #1/-3.0);   % stealth type

        }

        {

          ifthenelse{#3 = 2}

          {

            fill[#2] (#1/2.0,0pt) -- (-0.5*#1, #1/3.0) -- (-0.5*#1, #1/-3.0);   % latex type

          }

          {

            ifthenelse{#3 = 3}

            {

              % draw[thick, #2]  (-0.433*#1,#1/2) -- (0.433*#1, 0) -- (-0.433*#1,-#1/2);  % 60 degree arrow

              draw[semithick, #2]  (-0.533*#1,#1/2) -- (0.433*#1, 0) -- (-0.533*#1,-#1/2);  % 40 degree arrow

            }{}

          }

        }

      },

    },

    postaction={decorate}

  },

  ->-/.default={6pt black 1}

}





%==========================  Middle & pointing arrows ==========================%

%-------------------------------------------------------------------------------%

% usage: draw[-<-] path; or draw[-<-=6pt red 1] path;

%-------------------------------------------------------------------------------%

tikzset{

  -<-/.style args={#1 #2 #3}{

    decoration={

      markings,

      mark= at position 0.5 with

      {

        ifthenelse{#3 = 1}

        {

          fill[#2] (#1/6.0,0pt) -- (0.5*#1, #1/3.0) -- (-0.5*#1,0pt) -- (0.5*#1, #1/-3.0);   % stealth type

        }

        {

          ifthenelse{#3 = 2}

          {

            fill[#2] (#1/-2.0,0pt) -- (0.5*#1, #1/3.0) -- (0.5*#1, #1/-3.0);   % latex type

          }

          {

            ifthenelse{#3 = 3}

            {

              % draw[thick, #2]  (-0.433*#1,#1/2) -- (0.433*#1, 0) -- (-0.433*#1,-#1/2);  % 60 degree arrow

              draw[semithick, #2]  (0.533*#1,#1/2) -- (-0.433*#1, 0) -- (0.533*#1,-#1/2);  % 40 degree arrow

            }{}

          }

        }

      },

    },

    postaction={decorate}

  },

  -<-/.default={6pt black 1}

}





begin{document}



begin{tikzpicture}

draw[step=0.5cm, help lines, LightSkyBlue] (-7,-7) grid (7,7);

node (pol) [

  draw,

  minimum size=0.9textwidth,

  regular polygon, regular polygon sides=21,

  rotate=270,

  ]{};

foreach x/y/i in {1/2/1,3/4/1,5/6/2,7/8/2,9/10/3,11/12/3}

  path[auto=right, ->-]

    (pol.corner x)--(pol.corner y)

      node[midway]{$alpha_ {i}$};

foreach x/y/i in {2/3/1,4/5/1,6/7/2,8/9/2,10/11/3,12/13/3}

  path[auto=right, -<-]

    (pol.corner x)--(pol.corner y)

      node[midway]{$beta_ {i}$};

 foreach x/y/i in {13/14/1, 15/16/1, 16/17/2,18/19/2,19/20/3,21/1/3}

  path[auto=right]

    (pol.corner x)--(pol.corner y)

      node[midway]{$xi_ {i}$};

      foreach x/y/i in {14/15/1,17/18/2,20/21/3}

  path[auto=right]

    (pol.corner x)--(pol.corner y)

      node[midway]{$rho_ {i}$};

end{tikzpicture}





end{document}

As as a starting point, following code, based on my another answer How to draw all (or some) symmetries axes of a regular polygon, maybe useful.

documentclass{article}

usepackage{tikz}

usetikzlibrary{shapes.geometric, calc}

usetikzlibrary{decorations.markings}

usepackage{ifthen}

begin{document}



begin{tikzpicture}[scale=3]

defrps{21} % regular polygon sides

node (a) 

[draw,  blue!0!black,rotate=90,minimum size=3cm,regular polygon, regular polygon sides=rps] at (0, 0) {}; 



draw (a);

pgfmathtruncatemacro{rpslast}{rps+1};

foreach x in {1,2,...,rps}{

%foreach y in {1,2,...,rpslast}{

pgfmathtruncatemacro{y}{x+1};

ifnumy < rpslast

  begin{scope}[thin,decoration={

    markings,

    mark=at position 0.5 with {arrow{>}}}

    ] 

    draw[postaction={decorate}] (a.corner x)--(a.corner y);

    draw[postaction={decorate}] (a.corner rps)--(a.corner 1);       

end{scope}

    else

fi

}

end{tikzpicture}

end{document}