Producing a Commutative Diagram in the Shape of a Dodecagon

Question

I am trying to produce a diagram in the shape of a dodecagon, but using the approach I am more comfortable with I would need to be able to change the separation of individual pairs of columns and rows. Is that possible in TikZ-cd?

I would prefer to solve this problem using only TikZ-cd, but if that is not possible I would accept an answer offering an alternative method.

Here is my initial attempt at a dodecagon:

\documentclass{report}

\usepackage{tikz-cd}
\usepackage{caption}

\begin{document}

\begin{figure}
\centering
\begin{tikzcd}[column sep=1cm, row sep=1cm]
    &   &   c_{0}\arrow{r}\arrow{drr}   &   c_{1}\arrow{dr}\arrow{ddrr} &   &   \\
    &   c_{11}\arrow{ur}\arrow{urr} &   &   &    c_{2}\arrow{dr}\arrow{ddr}  &  \\
    c_{10}\arrow{ru}\arrow{rruu}     &  &   &   &   &    c_{3}\arrow{d}\arrow{ddl}   \\
    c_{9}\arrow{u}\arrow{uur}   &   &   &   &   &    c_{4}\arrow{dl}\arrow{ddll}     \\
    &    c_{8}\arrow{ul}\arrow{uul}     &   &   &    c_{5}\arrow{dl}\arrow{dll}  &    \\
    &   &   c_{7}\arrow{ul}\arrow{uull} &   c_{6}\arrow{l}\arrow{ull}   &   &
\end{tikzcd}
\caption*{Dodecagon}
\end{figure}

\end{document}

If it helps, the separation between the 1º and 2º columns and between the 5º and 6º must be reduced to 0,5cm, while the separation between the 2º and 3º columns and the 4º and 5º must be reduced to 0,8660254cm. The same must be done for the rows.

(EDIT: I found out how to change the separations of individual pairs of columns and rows, but the resulting diagram still does not look like a regular dodecagon...

\documentclass{report}

\usepackage{tikz-cd}
\usepackage{caption}

\begin{document}

\begin{figure}
\centering
\begin{tikzcd}
    &[0.5cm]    &[0.8660254cm]  c_{0}\arrow{r}\arrow{drr}   &[1cm]  c_{1}\arrow{dr}\arrow{ddrr} &[0.8660254cm]  &[0.5cm]    \\[0.5cm]
    &   c_{11}\arrow{ur}\arrow{urr} &   &   &    c_{2}\arrow{dr}\arrow{ddr}  &  \\[0.8660254cm]
    c_{10}\arrow{ru}\arrow{rruu}     &  &   &   &   &    c_{3}\arrow{d}\arrow{ddl}   \\[1cm]
    c_{9}\arrow{u}\arrow{uur}   &   &   &   &   &    c_{4}\arrow{dl}\arrow{ddll}     \\[0.8660254cm]
    &    c_{8}\arrow{ul}\arrow{uul}     &   &   &    c_{5}\arrow{dl}\arrow{dll}  &    \\[0.5cm]
    &   &   c_{7}\arrow{ul}\arrow{uull} &   c_{6}\arrow{l}\arrow{ull}   &   &
\end{tikzcd}
\caption*{Dodecagon}
\end{figure}

\end{document}

I assume either I made a mistake in my calculations or I misunderstood some technical aspect of the package TikZ-cd...)

Answer 1

New answer

Here is a dodecagon diagram built in pure Tikz with the chains library which is compilable with all engines (LaTeX, pdfLaTeX, XeLaTeX, LuaLaTeX).

Updated code (on request of OP)

Here, I placed indexed labels for the arrows inside the dodecagon and the same label for the others.

For the internal arrows, I chose these options:

font=\tiny,fill=white,outer sep=0pt,inner sep=1pt

and for you to understand the difference for the others with these options:

font=\scriptsize,auto=right,outer sep=0pt,inner sep=1pt 

If any of them require explanation, say so.

\documentclass[tikz, margin=3mm]{standalone}
\usetikzlibrary {chains}
\usetikzlibrary{arrows.meta}
\begin{document}

\begin{tikzpicture}[start chain= dodecagon placed {at=(120+\tikzchaincount*-30:2.5)}]
\foreach \i in {0,...,11}
    {\node [on chain] {$c_{\i}$};
    }
\foreach \i [evaluate={
            \next=int(1+mod({\i},12));
            \nextnext=int(1+mod({\i+1},12));}] 
        in {1,...,12}{
\draw[->] (dodecagon-\i)--node[font=\tiny,fill=white,outer sep=0pt,inner sep=1pt]{x}(dodecagon-\next);
\draw[->] (dodecagon-\i)to[bend right=20]node[font=\scriptsize,auto=right,outer sep=0pt,inner sep=1pt]{$l_{\i}$}(dodecagon-\nextnext);
}

\end{tikzpicture}
\end{document}

Old code

\documentclass[tikz, margin=3mm]{standalone}
\usetikzlibrary {chains}
\usetikzlibrary{arrows.meta}
\begin{document}

\begin{tikzpicture}[start chain= dodecagon placed {at=(120+\tikzchaincount*-30:2.5)},>={Stealth[round,sep]}]
\foreach \i in {0,...,11}
    {\node [on chain] {$c_{\i}$};
    }
\foreach \i [evaluate={
            \next=int(1+mod({\i},12));
            \nextnext=int(1+mod({\i+1},12));}] 
        in {1,...,12}{
\draw[->] (dodecagon-\i)--(dodecagon-\next);
\draw[->] (dodecagon-\i)to[bend right=15](dodecagon-\nextnext);
}

\end{tikzpicture}
\end{document}

Old answer :

Here is a graph created with Tikz (but not with tikz-cd) using the circular library which must be compiled with Lualatex.

\documentclass[border=5mm]{standalone}
\usepackage{tikz}
\usetikzlibrary {graphs,graphdrawing} 
\usegdlibrary {circular}
\usetikzlibrary{arrows.meta,bending}
\begin{document}
\begin{tikzpicture}[>={Stealth[round,sep]}]
\graph [simple necklace layout,
 node distance=1.5cm,
grow'=south,
math nodes,
edges={>={Stealth[round,sep,bend]}}]
{ c_0 -> c_1 -> c_2  -> c_3 -> c_4 -> c_5 -> c_6 -> c_7 -> c_8 -> c_9 -> c_{10} -> c_{11} -> c_0};

\graph [use existing nodes,
math nodes,
edges={bend right=15,>={Stealth[round,sep,bend]}}]{
c_1 -> c_3 -> c_5  -> c_7 -> c_9 -> c_{11} -> c_1,c_2 -> c_4 -> c_6 -> c_8 -> c_{10}->c_0
 };
\end{tikzpicture}
\end{document}

Answer 2

Just plain TikZ, all connections, no hard-coded values but just loops, everything in a single path. Works with all standard compilers (pdflatex, xelatex, lualatatex) and can thus be used in a paper that is to be submitted to the arXiv, say.

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{arrows.meta,bending}
\begin{document}
\begin{tikzpicture}
 \path[every edge/.append style={-{Stealth[bend]}}] foreach \X in {0,...,11}
 { (105-\X*30:4) node (c\X) {$c_{\X}$}}
  foreach \X [remember=\X as \LastX (initially 11),
    evaluate=\X as \LLastX using {int(Mod(\X+10,12))}] in {0,...,11}
  { (c\LastX) edge (c\X)
  \ifodd\X
   (c\LLastX) edge[bend left=60] (c\X)
  \else
   (c\LLastX) edge[bend right=5] (c\X) 
  \fi};
\end{tikzpicture}
\end{document}