    \begin{tikzpicture}%
    	[x={(240:2cm)},
    	y={(0:2cm)},
    	z={(120:2cm)},
        scale=0.3]

    \coordinate (w1) at (3,0,0);    
    \coordinate (w2) at (0,3,0);    
    \coordinate (w3) at (0,0,3);    
        
    \def\tilepositions{
    0/0/0 ,
    1/0/0 ,
    2/0/0 ,
    0/1/0 ,
    1/1/0 ,
    2/1/0 ,
    0/2/0 ,
    1/2/0 ,
    2/2/0 ,
    0/3/0 ,
    1/3/0 ,
    2/3/0 ,
    %
    0/0/1 ,    
    0/1/1 ,    
    0/2/1 ,    
    0/3/1 ,    
    0/0/2 ,    
    0/1/2 ,    
    0/2/2 ,    
    0/3/2 ,
    %
    1/0/1 ,
    2/0/1 ,
    1/0/2 ,
    2/0/2 
    }

    \node (132) at (1,3,2) {};
    \node (213) at (2,1,3) {};
    \node (231) at (2,3,1) {};
    \node (312) at (3,1,2) {};
    \node (321) at (3,2,1) {};

    % Central hexagon
    \draw[draw=white, fill=blue!10] (1,2,3) -- (2,1,3) -- (3,1,2) -- (3,2,1) -- (2,3,1) -- (1,3,2) -- cycle;
    
    %fundamental tile:
    \foreach \a/\b/\c in \tilepositions{
        \begin{scope}[shift={($\a*(3,0,0)+\b*(0,3,0)+\c*(0,0,3)$)}]
            \node (123) at (1,2,3) {
            \pgfmathparse{int(1+2*\a-1*\b-1*\c)}\ifthenelse{-1 < \pgfmathresult}{\pgfmathresult}{\pgfmathparse{int(neg(1+2*\a-1*\b-1*\c))}$\bar\pgfmathresult$}%
            \pgfmathparse{int(2-1*\a+2*\b-1*\c)}\ifthenelse{-1 < \pgfmathresult}{\pgfmathresult}{\pgfmathparse{int(neg(2-1*\a+2*\b-1*\c))}$\bar\pgfmathresult$}%
            \pgfmathparse{int(3-1*\a-1*\b+2*\c)}\ifthenelse{-1 < \pgfmathresult}{\pgfmathresult}{\pgfmathparse{int(neg(3-1*\a-1*\b+2*\c))}$\bar\pgfmathresult$}%
            };
            \node (132) at (1,3,2) {
            \pgfmathparse{int(1+2*\a-1*\b-1*\c)}\ifthenelse{-1 < \pgfmathresult}{\pgfmathresult}{\pgfmathparse{int(neg(1+2*\a-1*\b-1*\c))}$\bar\pgfmathresult$}%
            \pgfmathparse{int(3-1*\a+2*\b-1*\c)}\ifthenelse{-1 < \pgfmathresult}{\pgfmathresult}{\pgfmathparse{int(neg(3-1*\a+2*\b-1*\c))}$\bar\pgfmathresult$}%
            \pgfmathparse{int(2-1*\a-1*\b+2*\c)}\ifthenelse{-1 < \pgfmathresult}{\pgfmathresult}{\pgfmathparse{int(neg(2-1*\a-1*\b+2*\c))}$\bar\pgfmathresult$}%
            };
            % \node (123) at (1,2,3) {};
            \node (213) at (2,1,3) {};
            % \node (132) at (1,3,2) {};
            \node (231) at (2,3,1) {};
            \node (312) at (3,1,2) {};
            \node (321) at (3,2,1) {};
        
            % \draw[blue] (123) -- (213) -- (312) -- (321) -- (231) -- (132) -- (123);      
            \draw[blue] (213) -- (123) -- (132) -- (231);      
        \end{scope}
        }            

    \end{tikzpicture}   