\begin{tikzpicture}[x=1cm,y=1cm]
\begin{scope}
  \foreach \j in {0,...,5}
    \coordinate (u\j) at ({60*\j}:1.12);
  \foreach \j in {0,...,5}{
    \pgfmathtruncatemacro{\nextj}{mod(\j+1,6)}
    \draw[fold edge] (u\j)--(u\nextj);
  }
  \draw[marked edge] (u0)--(u1);
  \foreach \j in {0,...,5}{
    \ifodd\j \node[part B] at (u\j) {};
    \else \node[part A] at (u\j) {};\fi
    \node[font=\small] at ({60*\j}:1.35) {$\j$};
  }
  \node[diagram label] at (0,-2.7) {$H=C_6$};
\end{scope}
\draw[diagram arrow] (1.95,0)--(3.5,0);
\node[diagram label] at (2.725,.32) {Fiedler map $p$};
\begin{scope}[shift={(6,0)}]
  \fill[foldgreen!11] (0,0)--(0:2.12) arc[start angle=0,end angle=60,radius=2.12]--cycle;
  \foreach \angle in {0,60,120}
    \draw[mirror] (\angle:2.3)--({180+\angle}:2.3);
  \draw[draw=foldgreen!80,line width=.9pt] (0,0)--(0:2.25);
  \draw[draw=foldgreen!80,line width=.9pt] (0,0)--(60:2.25);
  \foreach \j in {0,...,5}
    \coordinate (p\j) at ({60*\j}:1.5);
  \foreach \j in {0,...,5}{
    \pgfmathtruncatemacro{\nextj}{mod(\j+1,6)}
    \draw[fold edge] (p\j)--(p\nextj);
  }
  \draw[marked edge] (p0)--(p1);
  \foreach \j in {0,...,5}{
    \ifodd\j \node[part B] at (p\j) {};
    \else \node[part A] at (p\j) {};\fi
  }
  \node[font=\small,anchor=north west] at (p0) {$x=p(0)$};
  \node[font=\small,anchor=south,fill=white,inner sep=1.5pt]
    at (.75,1.38) {$y=p(1)$};
  \foreach \j in {2,...,5}
    \node[font=\scriptsize,fill=white,inner sep=1pt]
      at ({60*\j}:1.78) {$p(\j)$};
  \fill[foldgray] (0,0) circle[radius=1.2pt];
  \node[font=\scriptsize,anchor=north west] at (.03,-.04) {$\mathbf0$};
  \node[font=\small,text=foldgreen] at (30:1.86) {$\overline C$};
  \node[font=\scriptsize,text=foldgreen,anchor=south west]
    at (2.28,.08) {$s_1$};
  \node[font=\scriptsize,text=foldgreen,anchor=west] at (1.18,1.98) {$s_2$};
  \node[diagram label] at (0,-2.7) {$W=\Sym(3)$};
\end{scope}
\end{tikzpicture}