\begin{tikzcd}[row sep={0.0*\the\DL,between origins}, column sep={0.0*\the\DL,between origins}, background color=backgroundColor, ampersand replacement=\&]
\&[1.73205081*\OneCm]
\&[1.73205081*\OneCm]
\text{1-3}
\&[1.73205081*\OneCm]
\&[1.73205081*\OneCm]
\\[2.0*\OneCm]
\text{2-1}
\&[1.73205081*\OneCm]
\&[1.73205081*\OneCm]
\text{2-3}
\&[1.73205081*\OneCm]
\&[1.73205081*\OneCm]
\text{2-5}
\\[1.0*\OneCm]
\&[1.73205081*\OneCm]
\text{3-2}
\&[1.73205081*\OneCm]
\&[1.73205081*\OneCm]
\text{3-4}
\&[1.73205081*\OneCm]
\\[2.0*\OneCm]
\&[1.73205081*\OneCm]
\text{4-2}
\&[1.73205081*\OneCm]
\&[1.73205081*\OneCm]
\text{4-4}
\&[1.73205081*\OneCm]
\\[1.0*\OneCm]
\text{5-1}
\&[1.73205081*\OneCm]
\&[1.73205081*\OneCm]
\text{5-3}
\&[1.73205081*\OneCm]
\&[1.73205081*\OneCm]
\text{5-5}
\\[2.0*\OneCm]
\&[1.73205081*\OneCm]
\&[1.73205081*\OneCm]
\text{6-3}
\&[1.73205081*\OneCm]
\&[1.73205081*\OneCm]
% Arrows
\arrow[from=1-3,to=2-1,"1"']%
\arrow[from=2-1,to=5-1,"2"']%
\arrow[from=5-1,to=6-3,"3"']%
%
\arrow[from=1-3,to=2-5,"4"]%
\arrow[from=2-5,to=5-5,"5"]%
\arrow[from=5-5,to=6-3,"6"]%
%
\arrow[from=2-3,to=3-2,"1'"description]%
\arrow[from=3-2,to=4-2,"2'"description]%
\arrow[from=4-2,to=5-3,"3'"description]%
%
\arrow[from=2-3,to=3-4,"4'"description]%
\arrow[from=3-4,to=4-4,"5'"description]%
\arrow[from=4-4,to=5-3,"6'"description]%
%
\arrow[from=1-3,to=2-3,"a"description]%
\arrow[from=2-1,to=3-2,"b"description]%
\arrow[from=2-5,to=3-4,"c"description]%
\arrow[from=5-1,to=4-2,"d"description]%
\arrow[from=5-5,to=4-4,"e"description]%
\arrow[from=5-3,to=6-3,"f"description]%
\end{tik-zcd}
To make the diagram larger, one could use e.g.
and replace all instances of \OneCm with \TwoCm in the code above.