\begin{tikzpicture}[x=1cm,y=1cm,font=\small]
  \foreach \i in {0,1,2,3}{
    \pgfmathsetmacro{\x}{1.75*\i}
    \draw[foldgray,rounded corners=3pt] (\x-.56,-.6) rectangle (\x+.56,.6);
    \foreach \j/\u/\v in {0/-.23/.23,1/.23/.23,2/-.23/-.23,3/.23/-.23}{
      \ifnum\i<3
        \ifnum\j<2
          \node[circle,draw=foldorange,fill=foldorange,inner sep=0pt,minimum size=5.5pt] at (\x+\u,\v) {};
        \else
          \node[part B] at (\x+\u,\v) {};
        \fi
      \else
        \node[part B] at (\x+\u,\v) {};
      \fi
    }
    \node at (\x,-.91) {$X_{\the\numexpr\i+1\relax}$};
  }
  \node[align=center] at (2.625,1.15) {one block: two points in each\\of three classes};
  \node[align=center] at (2.625,-1.65) {folds act within classes\\minimum point image: four};
  \draw[diagram arrow] (6.15,0) -- (7.65,0);
  \node[align=center,font=\footnotesize] at (6.9,.69) {retain the\\support};
  \foreach \i/\x/\y in {0/8.4/.45,1/9.65/.45,2/8.4/-.45,3/9.65/-.45}{
    \ifnum\i<3
      \node[circle,draw=foldorange,fill=foldorange,inner sep=0pt,minimum size=7pt] at (\x,\y) {};
    \else
      \node[part B,minimum size=7pt] at (\x,\y) {};
    \fi
    \node[font=\footnotesize] at (\x,\y-.27) {$X_{\the\numexpr\i+1\relax}$};
  }
  \node[align=center] at (9.025,1.15) {all three-subsets\\of four classes};
  \node[align=center] at (9.025,-1.65) {the support automorphisms\\permute the four classes};
\end{tikzpicture}