mjhjmtu

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
usetikzlibraryshapes.geometric
begindocument

begintikzpicture

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]$rho_ i$;
endtikzpicture

enddocument

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 ------------------------------%
usepackageifthen
usepackagetikz
usetikzlibraryshapes.geometric
usetikzlibrarydecorations, 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



begindocument

begintikzpicture
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]$rho_ i$;
endtikzpicture


enddocument

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.

documentclassarticle
usepackagetikz
usetikzlibraryshapes.geometric, calc
usetikzlibrarydecorations.markings
usepackageifthen
begindocument

begintikzpicture[scale=3]
defrps21 % 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);
pgfmathtruncatemacrorpslastrps+1;
foreach x in 1,2,...,rps{
%foreach y in 1,2,...,rpslast
pgfmathtruncatemacroyx+1;
ifnumy < rpslast
 beginscope[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); 
endscope
 else
fi

endtikzpicture
enddocument