Making picture like a circle with pointing edges in tikz

Question

\documentclass[preview, tikz]{standalone}
\usepackage{graphicx}  
\usetikzlibrary{shapes.geometric,decorations.markings}
\begin{document}
\begin{tikzpicture}

    \draw (1, 0) to[bend left=45] (0.94, 0.34) to [bend left=45] (0.77,0.64);
    \draw (1, 0) to[bend right=45] (0.94, -0.34) to [bend right=45] (0.77,-0.64);
    \draw (-0.77,-0.64) to[bend right=45] (-0.94,-0.34) to [bend right=45] (-1,0);
    \draw (-1, 0) to[bend right=45] (-0.94, 0.34) to [bend right=45] (-0.77,0.64);

    \draw [thin,black] (-0.77,0.64) to[out=10,in=260] (-0.34,1);
    \draw [thin,black] (0.77,0.64) to[out=170,in=280] (0.34,1);

    \begin{scope}[dotted]
    \draw [thin,black] (0.77,-0.64) to[out=220,in=320] (-0.77,-0.64);
    \end{scope}

    \draw [thin,black] (-0.34,1) to[out=270,in=120] (-0.255,0.66);
    \draw [thin,black] (-0.255,0.66) to[out=60,in=260] (-0.17,1);
    \draw [thin,black] (-0.17,1) to[out=280,in=120] (-0.085,0.66);
    \draw [thin,black] (0.255,0.66) to[out=60,in=260] (0.34,1);

    \begin{scope}[dotted]
    \draw [thin,black] (-0.085,0.66) to [out=0,in=180] (0.255,0.66);
    \end{scope}

    \node[point, label=above:{\scalebox{0.5}{$\alpha_1$}}] at (-0.90,0.23) {};

    \node[point, label=above:{\scalebox{0.5}{$\beta_1$}}] at (-1,-0.15) {};
    \node[point, label=above:{\scalebox{0.5}{${\alpha^'}_1$}}] at (-1.03,-0.5) {};

    \node[point, label=above:{\scalebox{0.5}{${\beta^'}_1$}}] at (-0.91,-0.85) {};
    #######
    \node[point, label=above:{\scalebox{0.5}{${\alpha}_g$}}] at (0.91,-0.85) {};
    \node[point, label=above:{\scalebox{0.5}{${\beta}_g$}}] at (1.03,-0.5) {};
    \node[point, label=above:{\scalebox{0.5}{${\alpha^'}_g$}}] at (1,-0.15) {};
    \node[point, label=above:{\scalebox{0.5}{${\beta^'}_g$}}] at (0.90,0.21) {};
    #######
     \node[point, label=above:{\scalebox{0.3}{${\gamma}_1$}}] at (-0.49,0.54) {};
      \node[point, label=above:{\scalebox{0.3}{${\gamma^'}_r$}}] at (0.49,0.54) {};
      \node[point, label=above:{\scalebox{0.3}{${\gamma^'}_1$}}] at (-0.26,0.54) {};
      \node[point, label=above:{\scalebox{0.3}{${\gamma}_r$}}] at (0.26,0.54) {};

 \node[point, label=below:{\scalebox{0.3}{$\frac{2\pi}{m_1}$}}] at (-0.375,1) {};
 \node[point, label=below:{\scalebox{0.3}{$\frac{2\pi}{m_r}$}}] at (0.375,1) {};



\draw [thin,black] (-0.43,0.81) to[out=315,in=225] (-0.32,0.80);
\draw [thin,black] (0.31,0.80) to[out=315,in=225] (0.43,0.81);
\draw [thin,black] (-0.205,0.78) to[out=315,in=225] (-0.13,0.78);

\end{tikzpicture}
\end{document}

I want to adjust \gamma_2 and \gamma'_2 in the diagram but it is not getting adjust. Could anyone help me to sort it out. Thanks!