\begin{tikzpicture}[x=1cm,y=1cm,font=\small]
\node[font=\small\bfseries] at (0,4.55) {Source: distance four};
\node[font=\small\bfseries] at (6,4.55) {Target: distance at most two};
\coordinate (o) at (0,0);
\coordinate (x) at (-1.45,1.65);
\coordinate (y) at (1.45,1.65);
\coordinate (z) at (0,3.3);
\coordinate (ui) at (-.725,.825);
\coordinate (uj) at (.725,.825);
\coordinate (xu) at (-.725,2.475);
\coordinate (yu) at (.725,2.475);
\draw[fold edge] (o)--(ui)--(x)--(xu)--(z)--(yu)--(y)--(uj)--(o);
\foreach \name in {o,x,y,z}{\node[part A] at (\name) {};}
\foreach \name in {ui,uj,xu,yu}{\node[part B] at (\name) {};}
\node[below=4pt] at (o) {$0$};
\node[left=5pt] at (x) {$x$};
\node[right=5pt] at (y) {$y$};
\node[above=5pt] at (z) {$z=x+y$};
\node[left=5pt,font=\scriptsize] at (ui) {$U_i$};
\node[right=5pt,font=\scriptsize] at (uj) {$U_j$};
\node[left=5pt,font=\scriptsize] at (xu) {$x+U_j$};
\node[right=5pt,font=\scriptsize] at (yu) {$y+U_i$};
\draw[diagram arrow] (2.55,1.65)--(3.9,1.65)
 node[midway,above=5pt] {$\phi$};
\node[align=center,font=\scriptsize] at (3.22,.8)
 {$U_i,U_j$ both\\map to $U_k$};
\coordinate (K) at (6,1.65);
\coordinate (oo) at (6,0);
\coordinate (xx) at (4.8,2.8);
\coordinate (yy) at (7.2,2.8);
\coordinate (zz) at (7.5,.8);
\draw[fold edge] (oo)--(K)--(xx) (yy)--(K)--(zz);
\node[part B] at (K) {};
\foreach \name in {oo,xx,yy,zz}{\node[part A] at (\name) {};}
\node[left=4pt] at (K) {$U_k$};
\node[below=4pt] at (oo) {$0$};
\node[above=5pt,align=center] at (xx) {$x'$\\[-1pt]\scriptsize $b_k=0$};
\node[above=5pt,align=center] at (yy) {$y'$\\[-1pt]\scriptsize $b_k=1$};
\node[right=5pt] at (zz) {$z'\in U_k$};
\node[align=center,text=foldorange,font=\scriptsize] at (6,-.75)
 {a distance-preserving map\\cannot make this collapse};
\end{tikzpicture}