\begin{tikzpicture}[x=1cm,y=1cm,font=\small]
  \foreach \yy/\name/\desc in {
      0/{$I_2(m)$}/{$C_{2m}$},
      -1.15/{$B_d$}/{$S(Q_d)$},
      -2.3/{$H_3$}/{subdivided dodecahedron},
      -3.45/{$H_4$}/{subdivided $120$-cell},
      -4.6/{$F_4$}/{$24$-cell edge--triangle incidence}} {
    \node[anchor=east,font=\bfseries] at (-.5,\yy) {\name};
    \node[anchor=west] at (4.65,\yy) {\desc};
  }
  \draw[fold edge] (0,0)--(1.25,0);
  \node[part A,minimum size=6pt] at (0,0) {};
  \node[part A,draw=foldorange,fill=foldorange,minimum size=6pt] at (1.25,0) {};
  \node[fill=white,inner sep=2pt] at (.625,.22) {$m\ge4$};
  \foreach \yy/\diagramN/\edgeLabel in {-1.15/4/4,-2.3/3/5,-3.45/4/5} {
    \draw[fold edge] (0,\yy)--(1.1,\yy);
    \node[part A,minimum size=6pt] at (0,\yy) {};
    \node[part A,draw=foldorange,fill=foldorange,minimum size=6pt] at (1.1,\yy) {};
    \node[fill=white,inner sep=1.5pt] at (.55,\yy+.2) {$\edgeLabel$};
    \ifnum\diagramN=3
      \draw[fold edge] (1.1,\yy)--(2.2,\yy);
      \node[part A,draw=foldgray,fill=foldgray,minimum size=6pt] at (2.2,\yy) {};
    \else
      \draw[fold edge] (1.1,\yy)--(2.2,\yy)--(3.3,\yy);
      \node[part A,draw=foldgray,fill=foldgray,minimum size=6pt] at (2.2,\yy) {};
      \node[part A,draw=foldgray,fill=foldgray,minimum size=6pt] at (3.3,\yy) {};
    \fi
  }
  \draw[white,line width=3pt] (1.65,-1.15)--(2.75,-1.15);
  \node[fill=white,inner sep=2pt] at (2.2,-1.15) {$\cdots$};
  \draw[fold edge] (0,-4.6)--(1.1,-4.6)--(2.2,-4.6)--(3.3,-4.6);
  \node[part A,draw=foldgray,fill=foldgray,minimum size=6pt] at (0,-4.6) {};
  \node[part A,minimum size=6pt] at (1.1,-4.6) {};
  \node[part A,draw=foldorange,fill=foldorange,minimum size=6pt] at (2.2,-4.6) {};
  \node[part A,draw=foldgray,fill=foldgray,minimum size=6pt] at (3.3,-4.6) {};
  \node[fill=white,inner sep=1.5pt] at (1.65,-4.4) {$4$};
\end{tikzpicture}