Xrfgtjtk

I created this nice Polygon

using the following code

documentclass[margin=0pt]{standalone}

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

usepackage{ifthen}

usepackage{tikz}

usetikzlibrary{shapes.geometric}

usetikzlibrary{decorations, decorations.markings} 

usetikzlibrary{arrows, arrows.meta}



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

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

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

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

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

         decoration={markings,mark= at position 0.5 with {arrow{stealth}}, }, 

            postaction={decorate}, }, 

        ->-/.default= {0.5 6pt black }}





%==========================  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 {arrow[>=stealth]{<}}, }, 

        postaction={decorate}, }, 

    -<-/.default= {0.5 6pt black }}





    begin{document}

    begin{tikzpicture}

    %Polygon 12 Seiten

    node[fill=gray!10] (pol) [ 

    %draw, 

    minimum size=0.9textwidth, regular polygon, regular polygon sides=12, rotate=195 ]{};

    foreach x/y/i in {1/2/1,5/6/2,9/10/3} %alpha's

    draw[black!10!red,auto=right,->-]

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

    node[black!10!red,midway]{$alpha_{i}$};

    foreach x/y/i in {3/4/1,7/8/2,11/12/3} %inverse alpha's

    draw[black!10!red,auto=right,-<-]

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

    node[black!10!red,midway]{$alpha_{i}$};

    foreach x/y/i in {2/3/1,6/7/2,10/11/3} %beta's

    draw[black!10!blue,auto=right,->-]

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

    node[black!10!blue,midway]{$beta_ {i}$};

    foreach x/y/i in {4/5/1,8/9/2,12/1/3} %inverse beta's

    draw[black!10!blue,auto=right,-<-]

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

    node[black!10!blue,midway]{$beta_{i}$};



    %xi's

    draw[black!40!green,decoration={ markings, mark=at position 0.5 with {arrow{stealth}}}, postaction={decorate}]  

    (0,-5.44) --(-2.21,-0.63) node[midway, left] {$xi_1$} ;

    draw[black!40!green,decoration={ markings, mark=at position 0.5 with {arrow{stealth}}}, postaction={decorate}]  

    (0,-5.44) -- (0,-20pt) node[midway, left] {$xi_2$};

    draw[black!40!green,decoration={ markings, mark=at position 0.5 with {arrow{stealth}}}, postaction={decorate}] 

    (0,-5.44) -- (2.21,-0.63) node[midway, left] {$xi_3$};



    % 3 Kreise mit Beschriftung

    draw[violet,decoration={markings, mark=at position 0.26 with {arrow[>=stealth]{<}}},

    postaction={decorate},fill=white] (-2.5,0) circle (20pt)  ;

    node[violet,above] at (-2.5,20pt) {$rho_1$};

    draw[violet,decoration={markings, mark=at position 0.26 with {arrow[>=stealth]{<}}},

    postaction={decorate},fill=white] (0,0) circle (20pt);

    node[violet,above] at (0,20pt) {$rho_2$};

    draw[violet,decoration={markings, mark=at position 0.26 with {arrow[>=stealth]{<}}},

    postaction={decorate},fill=white] (2.5,0) circle (20pt);

    node[violet,above] at (2.5,20pt) {$rho_3$};



    end{tikzpicture}



end{document}

Now, I tried to copy and paste this code into my paper. Here is a minimal example

    documentclass[oneside, a4paper,12pt]{article}



usepackage{ifthen}

usepackage{tikz-cd}

usepackage{tikz}

usetikzlibrary{shapes.geometric}

usetikzlibrary{decorations, decorations.markings} 

usetikzlibrary{arrows, arrows.meta}

usetikzlibrary{matrix, arrows, decorations.pathmorphing}





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

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

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

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

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

        decoration={markings,mark= at position 0.5 with {arrow{stealth}}, }, 

        postaction={decorate}, }, 

    ->-/.default= {0.5 6pt black }}





%==========================  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 {arrow[>=stealth]{<}}, }, 

        postaction={decorate}, }, 

    -<-/.default= {0.5 6pt black }}





begin{document}





    begin{center}

        begin{tikzpicture}

        %Polygon 12 Seiten

        node[fill=gray!10] (pol) [ 

        %draw, 

        minimum size=0.9textwidth, regular polygon, regular polygon sides=12, rotate=195 ]{};

        foreach x/y/i in {1/2/1,5/6/2,9/10/3} %alpha's

        draw[black!10!red,auto=right,->-]

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

        node[black!10!red,midway]{$alpha_{i}$};

        foreach x/y/i in {3/4/1,7/8/2,11/12/3} %inverse alpha's

        draw[black!10!red,auto=right,-<-]

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

        node[black!10!red,midway]{$alpha_{i}$};

        foreach x/y/i in {2/3/1,6/7/2,10/11/3} %beta's

        draw[black!10!blue,auto=right,->-]

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

        node[black!10!blue,midway]{$beta_ {i}$};

        foreach x/y/i in {4/5/1,8/9/2,12/1/3} %inverse beta's

        draw[black!10!blue,auto=right,-<-]

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

        node[black!10!blue,midway]{$beta_{i}$};



        %xi's

        draw[black!40!green,decoration={ markings, mark=at position 0.5 with {arrow{stealth}}}, postaction={decorate}]  

        (0,-5.44) --(-2.21,-0.63) node[midway, left] {$xi_1$} ;

        draw[black!40!green,decoration={ markings, mark=at position 0.5 with {arrow{stealth}}}, postaction={decorate}]  

        (0,-5.44) -- (0,-20pt) node[midway, left] {$xi_2$};

        draw[black!40!green,decoration={ markings, mark=at position 0.5 with {arrow{stealth}}}, postaction={decorate}] 

        (0,-5.44) -- (2.21,-0.63) node[midway, left] {$xi_3$};



        % 3 Kreise mit Beschriftung

        draw[violet,decoration={markings, mark=at position 0.26 with {arrow[>=stealth]{<}}},

        postaction={decorate},fill=white] (-2.5,0) circle (20pt)  ;

        node[violet,above] at (-2.5,20pt) {$rho_1$};

        draw[violet,decoration={markings, mark=at position 0.26 with {arrow[>=stealth]{<}}},

        postaction={decorate},fill=white] (0,0) circle (20pt);

        node[violet,above] at (0,20pt) {$rho_2$};

        draw[violet,decoration={markings, mark=at position 0.26 with {arrow[>=stealth]{<}}},

        postaction={decorate},fill=white] (2.5,0) circle (20pt);

        node[violet,above] at (2.5,20pt) {$rho_3$};





        end{tikzpicture}

    end{center}





end{document}

But then it produces the following image

As you can see, the positioning of the green lines is not correct anymore.
I didn't scale the picture, so I have no idea what went wrong.

The problem are different font sizes (12pt in the main file and default 10pt font size in the diagram file as you use textwidth to size your polygon and this length depends on the document default font size. You can either remove the font size dependency, e.g. by changing textwidth with a explicit length (in the sub file it has a length of 345pt), or use the standalone package (!) in the main document with the obeyclassoptions option and then use includestandalone{filebasename} to include the diagram file. The standalone package then will switch to the default font size automatically when including the code in the subfile.

documentclass[oneside, a4paper, 12pt]{article}



usepackage[obeyclassoptions]{standalone}

usepackage{ifthen}

usepackage{tikz-cd}

usepackage{tikz}

usetikzlibrary{shapes.geometric}

usetikzlibrary{decorations, decorations.markings} 

usetikzlibrary{arrows, arrows.meta}

usetikzlibrary{matrix, arrows, decorations.pathmorphing}





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

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

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

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

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

        decoration={markings,mark= at position 0.5 with {arrow{stealth}}, }, 

        postaction={decorate}, }, 

    ->-/.default= {0.5 6pt black }}





%==========================  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 {arrow[>=stealth]{<}}, }, 

        postaction={decorate}, }, 

    -<-/.default= {0.5 6pt black }}





begin{document}





    begin{center}

    includestandalone{q470062_sub}% here q470062_sub.tex contains the TikZ picture, change to the used filename

    end{center}





end{document}

Further standalone package option can be helpful here, check the manual for the subpreambles option which collects the preambles of subfiles automatically.

If you load the adjustbox package with the export option before the standalone package, you can also use includestandalone[center]{q470062_sub} to center the content as well as other adjustbox key to modify the diagram in size etc.

If this is all too complicate for you then just decrease the font size for the tikzpicture again. Within a 12pt document the footnotesize macro gives you 10pt again. Place that directly before begin{tikzpicture} and make sure that there is a group around it, like it is now due to the center environment.

The comments and answer by Martin Scharrer have already analysed that your problem is caused by the different font size. Here a minimal invasive attempt to workaround the problem:

    documentclass[oneside, a4paper,12pt]{article}



usepackage{ifthen}

usepackage{tikz-cd}

usepackage{tikz}

usetikzlibrary{shapes.geometric}

usetikzlibrary{decorations, decorations.markings} 

usetikzlibrary{arrows, arrows.meta}

usetikzlibrary{matrix, arrows, decorations.pathmorphing}





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

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

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

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

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

        decoration={markings,mark= at position 0.5 with {arrow{stealth}}, }, 

        postaction={decorate}, }, 

    ->-/.default= {0.5 6pt black }}





%==========================  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 {arrow[>=stealth]{<}}, }, 

        postaction={decorate}, }, 

    -<-/.default= {0.5 6pt black }}





    begin{document}

    begin{center}

    begin{tikzpicture}

    %Polygon 12 Seiten

    node[fill=gray!10] (pol) [ 

    %draw, 

    minimum size=0.9textwidth, regular polygon, regular polygon sides=12, rotate=195 ]{};

    foreach x/y/i in {1/2/1,5/6/2,9/10/3} %alpha's

    draw[black!10!red,auto=right,->-]

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

    node[black!10!red,midway]{$alpha_{i}$};

    foreach x/y/i in {3/4/1,7/8/2,11/12/3} %inverse alpha's

    draw[black!10!red,auto=right,-<-]

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

    node[black!10!red,midway]{$alpha_{i}$};

    foreach x/y/i in {2/3/1,6/7/2,10/11/3} %beta's

    draw[black!10!blue,auto=right,->-]

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

    node[black!10!blue,midway]{$beta_ {i}$};

    foreach x/y/i in {4/5/1,8/9/2,12/1/3} %inverse beta's

    draw[black!10!blue,auto=right,-<-]

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

    node[black!10!blue,midway]{$beta_{i}$};



        coordinate(mycord) at (0,-6.15);



    %xi's

    draw[black!40!green,decoration={ markings, mark=at position 0.5 with {arrow{stealth}}}, postaction={decorate}]  

    (mycord) --(-2.21,-0.63) node[midway, left] {$xi_1$} ;

    draw[black!40!green,decoration={ markings, mark=at position 0.5 with {arrow{stealth}}}, postaction={decorate}]  

    (mycord) -- (0,-20pt) node[midway, left] {$xi_2$};

    draw[black!40!green,decoration={ markings, mark=at position 0.5 with {arrow{stealth}}}, postaction={decorate}] 

    (mycord) -- (2.21,-0.63) node[midway, left] {$xi_3$};



    % 3 Kreise mit Beschriftung

    draw[violet,decoration={markings, mark=at position 0.26 with {arrow[>=stealth]{<}}},

    postaction={decorate},fill=white] (-2.5,0) circle (20pt)  ;

    node[violet,above] at (-2.5,20pt) {$rho_1$};

    draw[violet,decoration={markings, mark=at position 0.26 with {arrow[>=stealth]{<}}},

    postaction={decorate},fill=white] (0,0) circle (20pt);

    node[violet,above] at (0,20pt) {$rho_2$};

    draw[violet,decoration={markings, mark=at position 0.26 with {arrow[>=stealth]{<}}},

    postaction={decorate},fill=white] (2.5,0) circle (20pt);

    node[violet,above] at (2.5,20pt) {$rho_3$};







    end{tikzpicture}

    end{center}



end{document}

I was able to remove the font size dependency by using (pol.corner 1).

The following code produces the desired result.

documentclass[oneside, a4paper,12pt]{article}



usepackage{ifthen}

usepackage{tikz-cd}

usepackage{tikz}

usetikzlibrary{shapes.geometric}

usetikzlibrary{decorations, decorations.markings} 

usetikzlibrary{arrows, arrows.meta}

usetikzlibrary{matrix, arrows, decorations.pathmorphing}





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

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

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

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

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

        decoration={markings,mark= at position 0.5 with {arrow{stealth}}, }, 

        postaction={decorate}, }, 

    ->-/.default= {0.5 6pt black }}





%==========================  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 {arrow[>=stealth]{<}}, }, 

        postaction={decorate}, }, 

    -<-/.default= {0.5 6pt black }}





begin{document}





    begin{center}

        begin{tikzpicture}

        %Polygon 12 Seiten

        node[fill=gray!10] (pol) [ 

        %draw, 

        minimum size=0.9textwidth, regular polygon, regular polygon sides=12, rotate=195 ]{};

        foreach x/y/i in {1/2/1,5/6/2,9/10/3} %alpha's

        draw[black!10!red,auto=right,->-]

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

        node[black!10!red,midway]{$alpha_{i}$};

        foreach x/y/i in {3/4/1,7/8/2,11/12/3} %inverse alpha's

        draw[black!10!red,auto=right,-<-]

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

        node[black!10!red,midway]{$alpha_{i}$};

        foreach x/y/i in {2/3/1,6/7/2,10/11/3} %beta's

        draw[black!10!blue,auto=right,->-]

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

        node[black!10!blue,midway]{$beta_ {i}$};

        foreach x/y/i in {4/5/1,8/9/2,12/1/3} %inverse beta's

        draw[black!10!blue,auto=right,-<-]

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

        node[black!10!blue,midway]{$beta_{i}$};



        %xi's

        draw[black!40!green,decoration={ markings, mark=at position 0.5 with {arrow{stealth}}}, postaction={decorate}]  

        (pol.corner 1) --(-2.21,-0.63) node[midway, left] {$xi_1$} ;

        draw[black!40!green,decoration={ markings, mark=at position 0.5 with {arrow{stealth}}}, postaction={decorate}]  

        (pol.corner 1) -- (0,-20pt) node[midway, left] {$xi_2$};

        draw[black!40!green,decoration={ markings, mark=at position 0.5 with {arrow{stealth}}}, postaction={decorate}] 

        (pol.corner 1) -- (2.21,-0.63) node[midway, left] {$xi_3$};



        % 3 Kreise mit Beschriftung

        draw[violet,decoration={markings, mark=at position 0.26 with {arrow[>=stealth]{<}}},

        postaction={decorate},fill=white] (-2.5,0) circle (20pt)  ;

        node[violet,above] at (-2.5,20pt) {$rho_1$};

        draw[violet,decoration={markings, mark=at position 0.26 with {arrow[>=stealth]{<}}},

        postaction={decorate},fill=white] (0,0) circle (20pt);

        node[violet,above] at (0,20pt) {$rho_2$};

        draw[violet,decoration={markings, mark=at position 0.26 with {arrow[>=stealth]{<}}},

        postaction={decorate},fill=white] (2.5,0) circle (20pt);

        node[violet,above] at (2.5,20pt) {$rho_3$};





        end{tikzpicture}

    end{center}





end{document}