\begin{tabular}{cc}
    \begin{tikzpicture}%
    	[x={(240:2cm)},
    	y={(0:2cm)},
    	z={(120:2cm)},
        scale=0.15]
    
    \coordinate (0) at (0,0,0);
    \coordinate (w1) at (3,0,0);    
    \coordinate (w2) at (0,3,0);    
    \coordinate (w3) at (0,0,3);    
    \coordinate (-w1) at (-3,0,0);
    \coordinate (-w2) at (0,-3,0);    
    \coordinate (-w3) at (0,0,-3);    
    
    \def\boundaryvertices{
    %This is the list of boundary vertices of the the hexagon paired to draw the edges of the triangular tiling 
    %diagonals:
    3/0/3 /0/0/3,
    3/0/2 /0/1/3,
    3/0/1 /0/2/3,
    3/0/0 /0/3/3,
    3/1/0 /0/4/3,
    3/2/0 /0/4/2,
    3/3/0 /0/4/1,
    3/4/0 /0/4/0,
    %antidiagonals
    3/0/3 /3/0/0,
    2/0/3 /3/1/0,
    1/0/3 /3/2/0,
    0/0/3 /3/3/0,
    0/1/3 /3/4/0,
    0/2/3 /2/4/0,
    0/3/3 /1/4/0,
    0/4/3 /0/4/0,
    %horizontal
    3/0/0 /3/4/0,
    3/0/1 /2/4/0,
    3/0/2 /1/4/0,
    3/0/3 /0/4/0,
    2/0/3 /0/4/1,
    1/0/3 /0/4/2,
    0/0/3 /0/4/3
    }
    
    %draws translates of hyperplanes H_ij:
        \foreach \a/\b/\c /\d/\e/\f in \boundaryvertices{
            \draw[blue] ($\a*(w1)+\b*(w2)+\c*(w3)$) -- ($\d*(w1)+\e*(w2)+\f*(w3)$);
            }
    %draws hyperpalnes H_ij:
    \draw[ultra thick] ($3*(w1)+0*(w2)+0*(w3)$) -- ($0*(w1)+3*(w2)+3*(w3)$);
    \draw[ultra thick] ($3*(w1)+0*(w2)+3*(w3)$) -- ($0*(w1)+4*(w2)+0*(w3)$);
    \draw[ultra thick] ($0*(w1)+0*(w2)+3*(w3)$) -- ($3*(w1)+3*(w2)+0*(w3)$);
    
    \draw[ultra thick, blue] (w1) -- (-w2) -- (w3) -- (-w1) -- (w2) -- (-w3) -- cycle;
    %  \draw (0) -- (w1);
    %  \draw (0) -- (w2);
    %  \draw (0) -- (w3);
    %  \draw (0) -- (-w1);
    %  \draw (0) -- (-w2);
    %  \draw (0) -- (-w3);
    \node[fill=white, draw=black, circle, inner sep=0.5pt] at (w1) {$\widetilde w_1$};
    \node[fill=white, draw=black, circle, inner sep=0.5pt] at (w2) {$\widetilde w_2$};
    \node[fill=white, draw=black, circle, inner sep=0.5pt] at (w3) {$\widetilde w_3$};
    \end{tikzpicture} 
    &
    \begin{tikzpicture}%
    	[x={(240:2cm)},
    	y={(0:2cm)},
    	z={(120:2cm)},
        scale=0.15]

    \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 
    }

    %fundamental tile:
    \foreach \a/\b/\c in \tilepositions{
        \begin{scope}[shift={($\a*(3,0,0)+\b*(0,3,0)+\c*(0,0,3)$)}]
            \draw[blue,fill=brown!15] (1,2,3) -- (2,1,3) -- (3,1,2) -- (3,2,1) -- (2,3,1) -- (1,3,2) -- (1,2,3);      
        \end{scope}
        }            

    % middle hexagon:
        \draw[ultra thick,blue] (1,2,3) -- (2,1,3) -- (3,1,2) -- (3,2,1) -- (2,3,1) -- (1,3,2) -- (1,2,3);      
    
    \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 ($3*(w1)$) {};
    
    \end{tikzpicture}   
\end{tabular}