\def\mylocalscale{0.8}
\def\mylocalblue{blue!30}
\def\mylocalviolet{violet}
\def\mylocalpathcolor{black}
\def\localTemplatePolygon{
 \coordinate (a) at (0,0);
\foreach \x in {-144,-72,0,72,144} {
   \begin{scope}[rotate=\x]
    \coordinate (\x) at (0,-1.25) {}; 
    \end{scope}
}
\draw[opacity=0.65] (-144) -- (-72) -- (0) -- (72) -- (144) -- (-144);
\draw (0) node [below, violet] {   $\mathbf v_1$};
\draw (72) node [right, blue] {    $\mathbf v_2$};
\draw (144) node [right] {   $v_3$};
\draw (-144) node [left] {   $v_4$};
\draw (-72) node [left] {   $v_5$};
\draw[opacity=0.4] (0) -- (144) (-144) -- (0);

\draw [fill=\mylocalblue,opacity=.5] (0) -- (144) -- (72) -- (0);

%\draw (-0.8,0) node [black] {$A$};
%\draw (0,0) node [black] {$B$};
%\draw (0.7,0) node [black] {$C$};
}

\begin{tikzpicture}[scale=\mylocalscale,font=\small]
 \coordinate (a) at (0,0);
\foreach \x in {-144,-72,0,72,144} {
   \begin{scope}[rotate=\x]
    \node (\x) at (0,-1.25) [fill,circle,inner sep=0.5pt] {};
   \end{scope}
}
\draw[opacity=0.65] (-144) -- (-72) -- (0) -- (72) -- (144) -- (-144);
\draw (0) node [below] {  $v_1$};
\draw (72) node [right] {    $v_2$};
\draw (144) node [right] {  $v_3$};
\draw (-144) node [left] {   $v_4$};
\draw (-72) node [left] {   $v_5$};
\draw[opacity=0.65] (0) -- (144) (-144) -- (0);
\draw[->-=.7,red,very thick, densely dotted] (-72) -- (144) node[left,pos=0.6]{$\gamma$};
\draw (0,-2.5) node {$T$ and \textcolor{red}{$\gamma$}};
\draw (0,-3) node {};
\draw (-0.4,-0.2) node[magenta] {$b$};
\draw (0.4,-0.2) node[black] {$a$};
\end{tikzpicture}
\begin{tikzpicture}[scale=\mylocalscale,font=\small]
\localTemplatePolygon
\draw[fill=\mylocalviolet,opacity=.6] (0) -- (-144) -- (-72) -- (0);
\draw [ultra thick, \mylocalpathcolor, ->-=0.5] (-72) -- (-144) node[pos=0.5,left] {\small $1$};
\draw [ultra thick, \mylocalpathcolor, ->-=0.5] (-144) -- (0) node[pos=0.3,right,magenta] {$b$};
\draw [ultra thick, \mylocalpathcolor, ->-=0.5] (0) -- (144) node[pos=0.7,left,black] {$a$};
\draw (0,-2.3) node []{$(t_1,t_2)=(\textcolor{violet}{A},\textcolor{blue}{C})$};
\draw (0,-3) node {$1\, b^{-1} \, a $};
\draw (-0.8,0) node [black] {$A$};
%\draw (0,0) node [black] {$B$};
\draw (0.7,0) node [black] {$C$};
\end{tikzpicture}
\begin{tikzpicture}[scale=\mylocalscale,font=\small]
\localTemplatePolygon
\draw[fill=\mylocalviolet,opacity=.6] (0) -- (144) -- (-144) -- (0);
\draw[ultra thick, \mylocalpathcolor, ->-=0.5] (-72) -- (0) node[pos=0.3,right, below] {\small $1$};
\draw[ultra thick, \mylocalpathcolor, ->-=0.5] (0) -- (-144) node[pos=0.6,left,magenta] {$b$};
\draw[ultra thick, \mylocalpathcolor, ->-=0.5] (-144) -- (144)node[pos=0.6,above] {\small $1$};
\draw (0,-2.3) node []{$(t_1,t_2)=(\textcolor{violet}{B},\textcolor{blue}{C})$};
\draw (0,-3) node {$1\, b^{-1} \, 1 $};

%\draw (-0.8,0) node [black] {$A$};
\draw (0,0) node [black] {$B$};
\draw (0.7,0) node [black] {$C$};
\end{tikzpicture}