thaumagramme.sty

\RequirePackage{tikz}
\usetikzlibrary{shapes.geometric, calc}

\newcommand\innernode[2][]{}
\newcommand\outernode[2][]{}
\newcommand\centernode[1][]{\node[#1] at (0,0)}
\newcommand\nodeangleindex[3]{}

\makeatletter
% Define a new environment for the non-starred version
\newenvironment{thaumagramm}[1][3]{%
    \begin{tikzpicture}
    % Define the radius of the circles
    \def\outerR{2}
    \def\innerR{1.5}
    % Draw the two concentric circles
    \draw (0,0) circle (\outerR);
    \draw (0,0) circle (\innerR);

    \renewcommand\nodeangleindex[3]{
      \pgfmathtruncatemacro{\nodeangle}{90-360/#1*(##2-1)}
      \node[rotate=\nodeangle-90,##1] at (\nodeangle:##3)
    }
    \renewcommand\outernode[2][]{\nodeangleindex{##1}{##2}{1.75}}
    \renewcommand\innernode[2][]{\nodeangleindex{##1}{##2}{0.8}}    
    
    % Define vertices of the polygram
    \foreach \x [evaluate=\x as \nodeangle using 90-(\x-1)*360/#1] in {1,...,#1} {
        \coordinate (inner\x) at (\nodeangle:\innerR);
    }
    
    % Draw each segment individually
    \foreach \x in {1,...,#1} {
        \pgfmathtruncatemacro{\nextx}{mod(\x,#1)+1}
        \draw (inner\x) -- (inner\nextx);
    }
}{
    \end{tikzpicture}
}

% Define a new environment for the starred version
\newenvironment{thaumagramm*}[1][3]{%
    \begin{tikzpicture}
    % Define the radius of the circles
    \def\outerR{2}
    \def\innerR{1.5}
    % Draw the two concentric circles
    \draw (0,0) circle (\outerR);
    \draw (0,0) circle (\innerR);

    \renewcommand\nodeangleindex[3]{
      \pgfmathtruncatemacro{\nodeangle}{90-360/#1*(##2-1)}
      \node[rotate=\nodeangle-90,##1] at (\nodeangle:##3)
    }
    \renewcommand\outernode[2][]{\nodeangleindex{##1}{##2}{1.75}}
    \renewcommand\innernode[2][]{\nodeangleindex{##1}{##2}{0.8}}

    
    % Define vertices of the polygram
    \foreach \x [evaluate=\x as \nodeangle using 90-(\x-1)*360/#1] in {1,...,#1} {
        \coordinate (inner\x) at (\nodeangle:\innerR);
    }
    
    % Draw each segment individually
    \pgfmathsetmacro{\oddedges}{mod(#1,2)}
    
    \pgfmathsetmacro{\step}{gcd(#1, #1/2)} % Calculate step for skipping vertices
    \ifnum1=\oddedges
    \foreach \x in {1,...,#1} {
      \pgfmathtruncatemacro{\nexttarget}{mod(\x-1+\step,#1)+1}
      \draw (inner\x) -- (inner\nexttarget);
    }
    \else
    \foreach \x in {1,...,#1} {
      \pgfmathtruncatemacro{\nexttarget}{mod(\x+1,#1)+1}
      \draw (inner\x) -- (inner\nexttarget);
    }
    \pgfmathsetmacro{\max}{#1/2+1}
%    \foreach \x in {2,...,#1/2+1} {
%      \pgfmathtruncatemacro{\nexttarget}{\x+1}
%      \draw (inner\x) -- (inner\nexttarget);
%    }    
    \fi
}{
    \end{tikzpicture}
}