[] (6.000000, 0.000000) arc (0.000000:-180.000000:0.750000);
[] (4.500000, 0.000000) arc (180.000000:0.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (6.000000, 0.000000) arc (0.000000:-180.000000:0.750000);
[] (4.500000, 0.000000) arc (180.000000:0.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{\mathbb{R}I_{2}}^{1/2}\langle 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (6.000000, 0.000000) arc (0.000000:180.000000:0.750000);
[] (4.500000, 0.000000) arc (0.000000:-180.000000:0.500000);
[] (3.500000, 0.000000) arc (180.000000:0.000000:1.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (6.000000, 0.000000) arc (0.000000:180.000000:0.750000);
[] (4.500000, 0.000000) arc (0.000000:-180.000000:0.500000);
[] (3.500000, 0.000000) arc (180.000000:0.000000:1.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{2}I_{4}}^{1/2}\langle 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (6.000000, 0.000000) arc (0.000000:-180.000000:0.750000);
[] (4.500000, 0.000000) arc (180.000000:0.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{4}I_{6}}^{1/2}\langle 2 \rangle $  (6.000000, 0.000000) ;

[] (4.000000, 0.000000) arc (180.000000:360.000000:0.750000);
[] (5.500000, 0.000000) arc (180.000000:0.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $ L_1 $;
[draw, rectangle, color=red, fill=white] (vert_1) at (1.000000,0.000000) $ C_2 $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $ C_3 $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $ C_1 $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $ C_1' $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $ C_3' $;
[draw, rectangle, color=red, fill=white] (vert_6) at (6.000000,0.000000) $ C_2' $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $ L_3 $;

\begin{equation*}\begin{split}
\left[\Gamma_{C_2'}\Gamma_{C_1'}\Gamma_{C_2'}^{-1} , \Gamma_{L_3} \right]=e
\end{split}
\end{equation*}

§.§.§ Vertex Number 8

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) – (6.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 7, 8 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) arc (180.000000:0.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) arc (180.000000:0.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{\mathbb{R}I_{2}}^{1/2}\langle 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (180.000000:0.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (180.000000:0.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{2}I_{4}}^{1/2}\langle 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) arc (180.000000:0.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{4}I_{6}}^{1/2}\langle 2 \rangle $  (6.000000, 0.000000) ;

[] (6.000000, 0.000000) – (7.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $ L_1 $;
[draw, rectangle, color=red, fill=white] (vert_1) at (1.000000,0.000000) $ C_2 $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $ C_3 $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $ C_1 $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $ C_1' $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $ C_3' $;
[draw, rectangle, color=red, fill=white] (vert_6) at (6.000000,0.000000) $ C_2' $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $ L_3 $;

\begin{equation*}\begin{split}
\left\{\Gamma_{C_2'}  , \Gamma_{L_3} \right\}=e
\end{split}
\end{equation*}

§.§.§ Vertex Number 9

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) – (3.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) – (3.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 7, 8 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) – (3.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) – (3.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{\mathbb{R}I_{2}}^{1/2}\langle 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) – (3.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (0.000000:-180.000000:0.750000);
[] (0.500000, 0.000000) arc (180.000000:0.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{2}I_{4}}^{1/2}\langle 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (3.000000, 0.000000) arc (0.000000:180.000000:0.750000);
[] (1.500000, 0.000000) arc (0.000000:-180.000000:0.500000);
[] (0.500000, 0.000000) arc (180.000000:0.000000:1.500000);
[] (3.500000, 0.000000) arc (0.000000:-180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{4}I_{6}}^{1/2}\langle 2 \rangle $  (6.000000, 0.000000) ;

[] (2.000000, 0.000000) arc (180.000000:0.000000:0.750000);
[] (3.500000, 0.000000) arc (0.000000:-180.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $ L_1 $;
[draw, rectangle, color=red, fill=white] (vert_1) at (1.000000,0.000000) $ C_2 $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $ C_3 $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $ C_1 $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $ C_1' $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $ C_3' $;
[draw, rectangle, color=red, fill=white] (vert_6) at (6.000000,0.000000) $ C_2' $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $ L_3 $;

\begin{equation*}\begin{split}
\left[\Gamma_{C_1}\Gamma_{C_3}\Gamma_{C_1}^{-1} , \Gamma_{C_2} \right]=e
\end{split}
\end{equation*}

§.§.§ Vertex Number 10

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) – (5.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 3, 4 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) – (5.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (180.000000:360.000000:1.250000);
[] (6.500000, 0.000000) arc (0.000000:180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 7, 8 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (180.000000:360.000000:1.750000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:0.500000);
[] (6.500000, 0.000000) arc (0.000000:-180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (180.000000:360.000000:1.750000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (3.000000, 0.000000) arc (180.000000:0.000000:0.750000);
[] (4.500000, 0.000000) arc (180.000000:360.000000:1.500000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{\mathbb{R}I_{2}}^{1/2}\langle 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) arc (180.000000:360.000000:1.250000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) arc (180.000000:360.000000:1.250000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{2}I_{4}}^{1/2}\langle 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (180.000000:360.000000:1.750000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{4}I_{6}}^{1/2}\langle 2 \rangle $  (6.000000, 0.000000) ;

[] (5.000000, 0.000000) arc (0.000000:180.000000:0.750000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:2.000000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $ L_1 $;
[draw, rectangle, color=red, fill=white] (vert_1) at (1.000000,0.000000) $ C_2 $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $ C_3 $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $ C_1 $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $ C_1' $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $ C_3' $;
[draw, rectangle, color=red, fill=white] (vert_6) at (6.000000,0.000000) $ C_2' $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $ L_3 $;

\begin{equation*}\begin{split}
\left[\Gamma_{L_3}^{-1}\Gamma_{C_1'}^{-1}\Gamma_{C_3'}\Gamma_{C_1'}\Gamma_{L_3} , \Gamma_{C_2'} \right]=e
\end{split}
\end{equation*}

§.§.§ Vertex Number 11

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) – (6.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 5, 6 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (180.000000:0.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 3, 4 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (180.000000:0.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 7, 8 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (180.000000:360.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (180.000000:360.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (3.000000, 0.000000) arc (180.000000:0.000000:0.750000);
[] (4.500000, 0.000000) arc (180.000000:360.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{\mathbb{R}I_{2}}^{1/2}\langle 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{2}I_{4}}^{1/2}\langle 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (180.000000:360.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{4}I_{6}}^{1/2}\langle 2 \rangle $  (6.000000, 0.000000) ;

[] (5.000000, 0.000000) arc (0.000000:180.000000:0.750000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:1.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $ L_1 $;
[draw, rectangle, color=red, fill=white] (vert_1) at (1.000000,0.000000) $ C_2 $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $ C_3 $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $ C_1 $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $ C_1' $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $ C_3' $;
[draw, rectangle, color=red, fill=white] (vert_6) at (6.000000,0.000000) $ C_2' $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $ L_3 $;

\begin{equation*}\begin{split}
\left\{\Gamma_{C_1'}^{-1}\Gamma_{C_3'}\Gamma_{C_1'}  , \Gamma_{L_3} \right\}=e
\end{split}
\end{equation*}

§.§.§ Vertex Number 12

[scale=1 , xshift=-100]
[] (1.000000, 0.000000) – (2.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (1.000000, 0.000000) – (2.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 5, 6 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (1.000000, 0.000000) – (2.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 3, 4 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (1.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (1.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 7, 8 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (1.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (1.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (1.000000, 0.000000) arc (180.000000:360.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{\mathbb{R}I_{2}}^{1/2}\langle 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (1.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (1.000000, 0.000000) arc (180.000000:0.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{2}I_{4}}^{1/2}\langle 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (1.000000, 0.000000) arc (180.000000:0.000000:1.250000);
[] (3.500000, 0.000000) arc (0.000000:-180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{4}I_{6}}^{1/2}\langle 2 \rangle $  (6.000000, 0.000000) ;

[] (3.000000, 0.000000) arc (0.000000:-180.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $ L_1 $;
[draw, rectangle, color=red, fill=white] (vert_1) at (1.000000,0.000000) $ C_2 $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $ C_3 $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $ C_1 $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $ C_1' $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $ C_3' $;
[draw, rectangle, color=red, fill=white] (vert_6) at (6.000000,0.000000) $ C_2' $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $ L_3 $;

\begin{equation*}\begin{split}
\left\{\Gamma_{C_1}  , \Gamma_{C_2} \right\}=e
\end{split}
\end{equation*}

§.§.§ Vertex Number 13

[scale=1 , xshift=-100]
[] (3.000000, 0.000000) – (4.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (3.000000, 0.000000) – (4.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (3.000000, 0.000000) – (4.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 5, 6 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (3.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 3, 4 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (180.000000:0.000000:0.750000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (180.000000:0.000000:0.750000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:1.500000);
[] (6.500000, 0.000000) arc (0.000000:180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 7, 8 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (180.000000:0.000000:0.750000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:2.000000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:0.500000);
[] (6.500000, 0.000000) arc (0.000000:-180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (180.000000:0.000000:0.750000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:2.000000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (180.000000:360.000000:0.750000);
[] (3.500000, 0.000000) arc (180.000000:0.000000:0.500000);
[] (4.500000, 0.000000) arc (180.000000:360.000000:1.500000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{\mathbb{R}I_{2}}^{1/2}\langle 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (180.000000:0.000000:0.750000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:2.000000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (0.000000:-180.000000:0.750000);
[] (0.500000, 0.000000) arc (180.000000:0.000000:1.500000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:2.000000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{2}I_{4}}^{1/2}\langle 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (3.000000, 0.000000) arc (0.000000:180.000000:0.750000);
[] (1.500000, 0.000000) arc (0.000000:-180.000000:0.500000);
[] (0.500000, 0.000000) arc (180.000000:0.000000:1.500000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:2.000000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{4}I_{6}}^{1/2}\langle 2 \rangle $  (6.000000, 0.000000) ;

[] (2.000000, 0.000000) arc (180.000000:0.000000:0.750000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:2.000000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $ L_1 $;
[draw, rectangle, color=red, fill=white] (vert_1) at (1.000000,0.000000) $ C_2 $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $ C_3 $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $ C_1 $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $ C_1' $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $ C_3' $;
[draw, rectangle, color=red, fill=white] (vert_6) at (6.000000,0.000000) $ C_2' $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $ L_3 $;

\begin{equation*}\begin{split}
\left[\Gamma_{L_3}^{-1}\Gamma_{C_1}\Gamma_{C_3}\Gamma_{C_1}^{-1}\Gamma_{L_3} , \Gamma_{C_2'} \right]=e
\end{split}
\end{equation*}

§.§.§ Vertex Number 14

[scale=1 , xshift=-100]
[] (6.000000, 0.000000) – (7.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (6.000000, 0.000000) – (7.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (6.000000, 0.000000) – (7.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (6.000000, 0.000000) arc (0.000000:-180.000000:0.750000);
[] (4.500000, 0.000000) arc (180.000000:0.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 5, 6 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (6.000000, 0.000000) arc (0.000000:180.000000:0.750000);
[] (4.500000, 0.000000) arc (0.000000:-180.000000:0.500000);
[] (3.500000, 0.000000) arc (180.000000:0.000000:1.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 3, 4 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (6.000000, 0.000000) arc (0.000000:180.000000:0.750000);
[] (4.500000, 0.000000) arc (0.000000:-180.000000:0.500000);
[] (3.500000, 0.000000) arc (180.000000:0.000000:1.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (6.000000, 0.000000) arc (0.000000:-180.000000:1.250000);
[] (3.500000, 0.000000) arc (180.000000:0.000000:1.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 7, 8 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (7.000000, 0.000000) arc (0.000000:-180.000000:1.750000);
[] (3.500000, 0.000000) arc (180.000000:0.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (7.000000, 0.000000) arc (0.000000:-180.000000:1.750000);
[] (3.500000, 0.000000) arc (180.000000:0.000000:0.500000);
[] (4.500000, 0.000000) arc (180.000000:360.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (7.000000, 0.000000) arc (0.000000:-180.000000:1.250000);
[] (4.500000, 0.000000) arc (0.000000:180.000000:0.500000);
[] (3.500000, 0.000000) arc (0.000000:-180.000000:0.500000);
[] (2.500000, 0.000000) arc (180.000000:0.000000:1.100000);
[] (4.700000, 0.000000) arc (180.000000:360.000000:0.650000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{\mathbb{R}I_{2}}^{1/2}\langle 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (7.000000, 0.000000) arc (0.000000:-180.000000:1.350000);
[] (4.300000, 0.000000) arc (180.000000:0.000000:0.850000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (7.000000, 0.000000) arc (0.000000:-180.000000:1.350000);
[] (4.300000, 0.000000) arc (180.000000:0.000000:0.850000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{2}I_{4}}^{1/2}\langle 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (7.000000, 0.000000) arc (0.000000:-180.000000:1.750000);
[] (3.500000, 0.000000) arc (180.000000:0.000000:0.500000);
[] (4.500000, 0.000000) arc (180.000000:360.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{4}I_{6}}^{1/2}\langle 2 \rangle $  (6.000000, 0.000000) ;

[] (7.000000, 0.000000) arc (0.000000:-180.000000:1.750000);
[] (3.500000, 0.000000) arc (180.000000:0.000000:1.000000);
[] (5.500000, 0.000000) arc (0.000000:-180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $ L_1 $;
[draw, rectangle, color=red, fill=white] (vert_1) at (1.000000,0.000000) $ C_2 $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $ C_3 $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $ C_1 $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $ C_1' $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $ C_3' $;
[draw, rectangle, color=red, fill=white] (vert_6) at (6.000000,0.000000) $ C_2' $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $ L_3 $;

\begin{equation*}\begin{split}
\left[\Gamma_{C_3'}\Gamma_{C_1'}\Gamma_{L_3}\Gamma_{C_1'}^{-1}\Gamma_{C_3'}^{-1} , \Gamma_{C_1'} \right]=e
\end{split}
\end{equation*}

§.§.§ Vertex Number 15

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) – (1.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 7, 8 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) – (1.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) – (1.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.250000);
[] (2.500000, 0.000000) arc (0.000000:180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.250000);
[] (2.500000, 0.000000) arc (0.000000:180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 5, 6 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.250000);
[] (2.500000, 0.000000) arc (0.000000:180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 3, 4 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.750000);
[] (3.500000, 0.000000) arc (0.000000:180.000000:0.500000);
[] (2.500000, 0.000000) arc (0.000000:-180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.750000);
[] (3.500000, 0.000000) arc (0.000000:180.000000:0.500000);
[] (2.500000, 0.000000) arc (0.000000:-180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 7, 8 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.750000);
[] (3.500000, 0.000000) arc (0.000000:180.000000:0.500000);
[] (2.500000, 0.000000) arc (0.000000:-180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.750000);
[] (3.500000, 0.000000) arc (0.000000:180.000000:0.500000);
[] (2.500000, 0.000000) arc (0.000000:-180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:2.250000);
[] (4.500000, 0.000000) arc (0.000000:180.000000:0.500000);
[] (3.500000, 0.000000) arc (0.000000:-180.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{\mathbb{R}I_{2}}^{1/2}\langle 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.750000);
[] (3.500000, 0.000000) arc (0.000000:180.000000:0.500000);
[] (2.500000, 0.000000) arc (0.000000:-180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.750000);
[] (3.500000, 0.000000) arc (0.000000:180.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{2}I_{4}}^{1/2}\langle 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.750000);
[] (3.500000, 0.000000) arc (0.000000:180.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{4}I_{6}}^{1/2}\langle 2 \rangle $  (6.000000, 0.000000) ;

[] (0.000000, 0.000000) arc (180.000000:360.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $ L_1 $;
[draw, rectangle, color=red, fill=white] (vert_1) at (1.000000,0.000000) $ C_2 $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $ C_3 $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $ C_1 $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $ C_1' $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $ C_3' $;
[draw, rectangle, color=red, fill=white] (vert_6) at (6.000000,0.000000) $ C_2' $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $ L_3 $;

\begin{equation*}\begin{split}
\left[\Gamma_{L_1} , \Gamma_{C_1} \right]=e
\end{split}
\end{equation*}

§.§.§ Vertex Number 16

[scale=1 , xshift=-100]
[] (1.000000, 0.000000) – (2.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 1, 2 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:0.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 7, 8 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:0.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:0.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 5, 6 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 3, 4 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 7, 8 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:2.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{\mathbb{R}I_{2}}^{1/2}\langle 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{2}I_{4}}^{1/2}\langle 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (0.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{4}I_{6}}^{1/2}\langle 2 \rangle $  (6.000000, 0.000000) ;

[] (0.000000, 0.000000) – (1.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $ L_1 $;
[draw, rectangle, color=red, fill=white] (vert_1) at (1.000000,0.000000) $ C_2 $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $ C_3 $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $ C_1 $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $ C_1' $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $ C_3' $;
[draw, rectangle, color=red, fill=white] (vert_6) at (6.000000,0.000000) $ C_2' $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $ L_3 $;

\begin{equation*}\begin{split}
\left\{\Gamma_{L_1}  , \Gamma_{C_2} \right\}=e
\end{split}
\end{equation*}

§.§.§ Vertex Number 17

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) – (3.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (0.000000:-180.000000:0.750000);
[] (0.500000, 0.000000) arc (180.000000:0.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 1, 2 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (0.000000:180.000000:0.750000);
[] (0.500000, 0.000000) arc (0.000000:-180.000000:0.500000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:1.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 7, 8 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (0.000000:180.000000:0.750000);
[] (0.500000, 0.000000) arc (0.000000:-180.000000:0.500000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:1.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (0.000000:180.000000:0.750000);
[] (0.500000, 0.000000) arc (0.000000:-180.000000:0.500000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:1.500000);
[] (2.500000, 0.000000) arc (180.000000:360.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (0.000000:-180.000000:1.250000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:1.500000);
[] (2.500000, 0.000000) arc (180.000000:360.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (0.000000:-180.000000:1.250000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:1.500000);
[] (2.500000, 0.000000) arc (180.000000:360.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 5, 6 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (0.000000:-180.000000:1.250000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:1.500000);
[] (2.500000, 0.000000) arc (180.000000:360.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 3, 4 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (3.000000, 0.000000) arc (0.000000:-180.000000:1.750000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:1.000000);
[] (1.500000, 0.000000) arc (180.000000:360.000000:0.500000);
[] (2.500000, 0.000000) arc (180.000000:0.000000:0.500000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (3.000000, 0.000000) arc (0.000000:-180.000000:1.750000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:1.000000);
[] (1.500000, 0.000000) arc (180.000000:360.000000:0.500000);
[] (2.500000, 0.000000) arc (180.000000:0.000000:0.500000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:1.500000);
[] (6.500000, 0.000000) arc (0.000000:180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 7, 8 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (3.000000, 0.000000) arc (0.000000:-180.000000:1.750000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:1.000000);
[] (1.500000, 0.000000) arc (180.000000:360.000000:0.500000);
[] (2.500000, 0.000000) arc (180.000000:0.000000:0.500000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:2.000000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:0.500000);
[] (6.500000, 0.000000) arc (0.000000:-180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (3.000000, 0.000000) arc (0.000000:-180.000000:1.750000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:1.000000);
[] (1.500000, 0.000000) arc (180.000000:360.000000:0.500000);
[] (2.500000, 0.000000) arc (180.000000:0.000000:0.500000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:2.000000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (0.000000:-180.000000:2.250000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:1.000000);
[] (1.500000, 0.000000) arc (180.000000:360.000000:1.000000);
[] (3.500000, 0.000000) arc (180.000000:0.000000:0.500000);
[] (4.500000, 0.000000) arc (180.000000:360.000000:1.500000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{\mathbb{R}I_{2}}^{1/2}\langle 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (3.000000, 0.000000) arc (0.000000:-180.000000:1.750000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:1.000000);
[] (1.500000, 0.000000) arc (180.000000:360.000000:0.500000);
[] (2.500000, 0.000000) arc (180.000000:0.000000:0.500000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:2.000000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (3.000000, 0.000000) arc (0.000000:-180.000000:1.750000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:0.500000);
[] (0.500000, 0.000000) arc (180.000000:360.000000:1.000000);
[] (2.500000, 0.000000) arc (0.000000:180.000000:0.500000);
[] (1.500000, 0.000000) arc (0.000000:-180.000000:0.400000);
[] (0.700000, 0.000000) arc (180.000000:0.000000:1.400000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:2.000000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{2}I_{4}}^{1/2}\langle 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (2.000000, 0.000000) arc (0.000000:-180.000000:1.250000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:0.500000);
[] (0.500000, 0.000000) arc (180.000000:360.000000:0.500000);
[] (1.500000, 0.000000) arc (180.000000:0.000000:0.500000);
[] (2.500000, 0.000000) arc (180.000000:360.000000:0.500000);
[] (3.500000, 0.000000) arc (0.000000:180.000000:1.100000);
[] (1.300000, 0.000000) arc (0.000000:-180.000000:0.300000);
[] (0.700000, 0.000000) arc (180.000000:0.000000:1.500000);
[] (3.700000, 0.000000) arc (180.000000:360.000000:1.900000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:1.250000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{4}I_{6}}^{1/2}\langle 2 \rangle $  (6.000000, 0.000000) ;

[] (1.000000, 0.000000) arc (0.000000:-180.000000:0.750000);
[] (-0.500000, 0.000000) arc (180.000000:0.000000:1.000000);
[] (1.500000, 0.000000) arc (180.000000:360.000000:0.500000);
[] (2.500000, 0.000000) arc (180.000000:0.000000:0.500000);
[] (3.500000, 0.000000) arc (180.000000:360.000000:2.000000);
[] (7.500000, 0.000000) arc (0.000000:180.000000:0.750000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $ L_1 $;
[draw, rectangle, color=red, fill=white] (vert_1) at (1.000000,0.000000) $ C_2 $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $ C_3 $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $ C_1 $;
[draw, rectangle, color=red, fill=white] (vert_4) at (4.000000,0.000000) $ C_1' $;
[draw, rectangle, color=red, fill=white] (vert_5) at (5.000000,0.000000) $ C_3' $;
[draw, rectangle, color=red, fill=white] (vert_6) at (6.000000,0.000000) $ C_2' $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $ L_3 $;

\begin{equation*}\begin{split}
\Gamma_{L_3}^{-1}\Gamma_{C_1}\Gamma_{C_2}\Gamma_{L_1}\Gamma_{C_2}\Gamma_{L_1}^{-1}\Gamma_{C_2}^{-1}\Gamma_{C_1}^{-1}\Gamma_{L_3}  = \Gamma_{C_2'}
\end{split}
\end{equation*}

§.§.§ Vertex Number 18

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) – (6.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, rectangle, color=red, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta_{I_{2}\mathbb{R}}^{1/2}\langle 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) – (6.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) – (6.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 1, 2 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) – (6.000000, 0.000000) ;
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 7, 8 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 4, 5 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 2, 3 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) arc (180.000000:360.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta^{2}\langle 6, 7 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (5.000000, 0.000000) arc (180.000000:0.000000:1.000000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 5, 6 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (180.000000:0.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_6) at (6.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_7) at (7.000000,0.000000) $  $;

[scale=1 , xshift=100]
[->] (0.000000, 0.000000) – node [above, midway] $ \Delta\langle 3, 4 \rangle $  (6.000000, 0.000000) ;

[scale=1 , xshift=-100]
[] (4.000000, 0.000000) arc (180.000000:0.000000:1.500000);
[draw, circle, color=black, fill=white] (vert_0) at (0.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_1) at (1.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_2) at (2.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_3) at (3.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_4) at (4.000000,0.000000) $  $;
[draw, circle, color=black, fill=white] (vert_5) at (5.000000,0.000000) $  $;