
    \begin{tikzpicture}%
    	[x={(240:2cm)},
    	y={(0:2cm)},
    	z={(120:2cm)},
        scale=0.23]

    \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,
    0/1/0,
    1/1/0,
    0/0/1,    
    0/1/1,    
    1/0/1
    }

    %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, 
    2/-1/0/purple, 0/2/-1/skyblue, -1/0/2/red, -2/1/0/yellow, 0/-2/1/bluishgreen, 1/0/-2/blue}
    
    \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 (n0) at (0,0,0) {$0$};
    \node (n1) at (w1) {$w_1$};
    \node (n2) at (w2) {$w_2$};
    \node (n3) at (w3) {$w_3$};
    \draw[dashed,->] (n0) -- (n1);
    \draw[dashed,->] (n0) -- (n2);
    \draw[dashed,->] (n0) -- (n3); 
        
    \node at ($2*(w1)-1*(w2)+0*(w3)$) {\small $2w_1-w_2$};
    \node at ($0*(w1)+2*(w2)-1*(w3)$) {\small $2w_2-w_3$};
    \node at ($-1*(w1)+0*(w2)+2*(w3)$) {\small $2w_3-w_1$};
    \end{tikzpicture}

