\begin{tikzcd}[row sep={4.0*\the\DL,between origins}, column sep={4.0*\the\DL,between origins}, background color=backgroundColor, ampersand replacement=\&]
1
\&
\&
2
\&
\\
\&
1'
\&
\&
2'
\\
3
\&
\&
\&
\\
\&
3'
\&
\&
4'
% 1-Arrows
% First Square
\arrow[from=1-1,to=3-1,"f"']%
\arrow[from=1-1,to=1-3,"g"]%
% Second Square
\arrow[from=2-2,to=4-2,"f'"{description},crossing over]%
\arrow[from=4-2,to=4-4,"h'"']%
\arrow[from=2-2,to=2-4,"g'"{description},crossing over]%
\arrow[from=2-4,to=4-4,"k'"]%
% Connecting Arrows
\arrow[from=1-1,to=2-2,"c_{1}"description]%
\arrow[from=1-3,to=2-4,"c_{2}"]%
\arrow[from=3-1,to=4-2,"c_{3}"']%
% Subdiagrams
\arrow[from=2-2,to=1-3,"\scriptstyle(1)"{rotate=-0.3,xslant=-0.903569337,yslant=0,xscale=7.0341,yscale=4.4454,xscale=0.225,yscale=0.225},phantom]%
\arrow[from=3-1,to=2-2,"\scriptstyle(2)"{rotate=-44.6,xslant=-0.965688775,yslant=0,xscale=8.6931,yscale=8.2852,xscale=0.15,yscale=0.15},phantom]%
\arrow[from=4-2,to=2-4,"\scriptstyle(3)"{rotate=0,xslant=0,yslant=0,xscale=1.5,yscale=1.5},phantom]%
\end{tikzcd}
\qquad
\begin{tikzcd}[row sep={4.0*\the\DL,between origins}, column sep={4.0*\the\DL,between origins}, background color=backgroundColor, ampersand replacement=\&]
1
\&
\&
2
\&
\\
\&
\&
\&
2'
\\
3
\&
\&
4
\&
\\
\&
3'
\&
\&
4'
% 1-Arrows
% First Square
\arrow[from=1-1,to=3-1,"f"']%
\arrow[from=3-1,to=3-3,"h"{description}]%
\arrow[from=1-1,to=1-3,"g"]%
\arrow[from=1-3,to=3-3,"k"{description}]%
% Second Square
\arrow[from=4-2,to=4-4,"h'"']%
\arrow[from=2-4,to=4-4,"k'"]%
% Connecting Arrows
\arrow[from=1-3,to=2-4,"c_{2}"]%
\arrow[from=3-1,to=4-2,"c_{3}"']%
\arrow[from=3-3,to=4-4,"c_{4}"description]%
% Subdiagrams
\arrow[from=1-1,to=3-3,"\scriptstyle(4)"{rotate=0,xslant=0,yslant=0,xscale=1.5,yscale=1.5},phantom]%
\arrow[from=3-3,to=2-4,"\scriptstyle(5)"{rotate=-44.6,xslant=-0.965688775,yslant=0,xscale=8.6931,yscale=8.2852,xscale=0.15,yscale=0.15},phantom]%
\arrow[from=4-2,to=3-3,"\scriptstyle(6)"{rotate=-0.3,xslant=-0.903569337,yslant=0,xscale=7.0341,yscale=4.4454,xscale=0.225,yscale=0.225},phantom]%
\end{tikzcd}