
    \begin{tikzpicture}%
    	[x={(240:2cm)},
    	y={(0:2cm)},
    	z={(120:2cm)},
        scale=0.131]

    \coordinate (w1) at (3,0,0);    
    \coordinate (w2) at (0,3,0);    
    \coordinate (w3) at (0,0,3);    

    % \node at (0,0,0) {0};
    \draw (1,2,3) -- (2,1,3) -- (3,1,2) -- (3,2,1) -- (2,3,1) -- (1,3,2) -- (1,2,3); 

    \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 
    }

    %fundamental tile:
    \foreach \a/\b/\c in \tilepositions{
        \begin{scope}[shift={($\a*(3,0,0)+\b*(0,3,0)+\c*(0,0,3)$)}]
            \draw[thick,draw=black,fill=orange] (1,2,3) -- (2,1,3) -- (3,1,2) -- (3,2,1) -- (2,3,1) -- (1,3,2) -- (1,2,3);      
            \node at (0,0,0) {$\a\b\c$};
        \end{scope}
        }            

    % shifts of the tiles
    \def\tileshifts{%0/0/0/brown, 
    3/-3/0/purple, 0/4/-2/skyblue, -2/0/3/red, 3/1/-2/blue, -2/4/1/yellow, 1/-3/3/bluishgreen}
    
    \foreach \d\e\f\tilecolor in \tileshifts{
        \begin{scope}[shift={($\d*(3,0,0)+\e*(0,3,0)+\f*(0,0,3)$)}]        
        
            \foreach \a/\b/\c in \tilepositions{
                \begin{scope}[shift={($\a*(3,0,0)+\b*(0,3,0)+\c*(0,0,3)$)}]
                    \draw[thick,draw=black,fill=\tilecolor] (1,2,3) -- (2,1,3) -- (3,1,2) -- (3,2,1) -- (2,3,1) -- (1,3,2) -- (1,2,3);      
                    % \node at (0,0,0) {$\a\b\c$};
                \end{scope}
                }            
            % \node at (0,0,0) {\d\e\f};
            % \node at (3,0,0) {\tilecolor};
        \end{scope}
        }
    % \node at (0,0,0) {$000$};
    \node at ($3*(w1)-3*(w2)+0*(w3)$) {$3\bar 3 0$};
    \node at ($0*(w1)+4*(w2)-2*(w3)$) {$0 4\bar 2$};
    \node at ($-2*(w1)+0*(w2)+3*(w3)$) {$\bar 2 0 3$};
    \end{tikzpicture}