Wie zeichnet man den Namen in die Mitte der Flächen eines Diagramms?

Question

Ich brauche bitte Ihre Hilfe, wie man den Namen in die Mitte der Flächen eines Diagramms und auch die äußere Fläche auf dieser Zeichnung zeichnet. Vielen Dank für Ihre Hilfe, Community. Ich habe hier den Code:

    \begin{tikzpicture}
        % Source : https://www.baeldung.com/cs/latex-drawing-graphs 
        % https://tex.stackexchange.com/questions/270543/draw-a-graph-in-latex-with-tikz
        % https://tex.stackexchange.com/questions/315456/colouring-graphs-tikz      
        % source ellipse : https://www.overleaf.com/learn/latex/LaTeX_Graphics_using_TikZ%3A_A_Tutorial_for_Beginners_(Part_1)%E2%80%94Basic_Drawing
        \draw  [fill = green!5!white]  (2,2) ellipse (7cm and 4cm);
        
        %\draw  [fill = green!5!white] 
        %       (-1,-2) .. controls (0,-3) .. (5,-2) .. controls (9,1) and (7,7) .. (4,7.5) .. controls (0,8) and (-4,8) .. (-1,-2) ;                                   
        
        \path
        ( 0  , 3 ) coordinate (1)
        ( 2.5, 4 ) coordinate (2)
        ( 5  , 3 ) coordinate (3)
        ( 3.5, 1 ) coordinate (4)
        ( 1  , 0 ) coordinate (5);      
        
        \draw [fill = violet] (1) to [out=125,in=90,looseness=2] (3);
        \draw [fill = yellow] (1) to [out=-120,in=-90,looseness=3] (4);     
        \draw (1) -- (3) ;  
        \draw [fill = orange] (2) -- (4) -- (5) -- (2);
        \draw [fill = cyan] (2) -- (3) -- (4) -- (2); 
        \draw [fill = pink] (1) -- (2) -- (5) -- (1);
        \draw (5) -- (1);
        \draw (2) -- (4);   
        \draw (2) -- (5);       
        
        \tikzstyle{vertex} = [draw,circle,fill=white,inner sep = 3pt]
        \node[vertex] [label = left: 1] at (1) {};
        \node[vertex] [label = above : 2] at (2) {};
        \node[vertex] [label = below: 3] at (3) {};
        \node[vertex] [label = right: 4] at (4) {};
        \node[vertex] [label = left: 5] at (5) {};
        %   \draw (0,0) arc (0:270:8mm);
        %   \draw (0,0) arc (0:315:1.75cm and 1cm); 
    \end{tikzpicture}    

meine Zeichnung sieht im Moment so aus:

Das gewünschte Ergebnis sollte bitte ungefähr so ​​aussehen:

Answer 1

mein Endergebnis

\begin{tikzpicture}
    % Source : https://www.baeldung.com/cs/latex-drawing-graphs 
    % https://tex.stackexchange.com/questions/270543/draw-a-graph-in-latex-with-tikz
    % https://tex.stackexchange.com/questions/315456/colouring-graphs-tikz      
    % source ellipse : https://www.overleaf.com/learn/latex/LaTeX_Graphics_using_TikZ%3A_A_Tutorial_for_Beginners_(Part_1)%E2%80%94Basic_Drawing
    \draw  [fill = green!5!white]  (2,2) ellipse (7cm and 4cm);
    
    %\draw  [fill = green!5!white] 
    %       (-1,-2) .. controls (0,-3) .. (5,-2) .. controls (9,1) and (7,7) .. (4,7.5) .. controls (0,8) and (-4,8) .. (-1,-2) ;                                   
    
    \path
    ( 0  , 3 ) coordinate (1) 
    ( 2.5, 4 ) coordinate (2)
    ( 5  , 3 ) coordinate (3)
    ( 3.5, 1 ) coordinate (4)
    ( 1  , 0 ) coordinate (5);      
    
    \draw [fill = violet] (1) to [out=125,in=90,looseness=2] (3);
    \draw [fill = yellow] (1) to [out=-120,in=-90,looseness=3] (4);     
    \draw (1) -- (3) ;  
    \draw [fill = orange] (2) -- (4) -- (5) -- (2);
    \draw [fill = cyan] (2) -- (3) -- (4) -- (2); 
    \draw [fill = pink] (1) -- (2) -- (5) -- (1);
    \draw (5) -- (1);
    \draw (2) -- (4);   
    \draw (2) -- (5);       
    
    \tikzstyle{vertex} = [draw,circle,fill=white,inner sep = 3pt]
    \node[vertex] [label = left: 1] at (1) {};
    \node[vertex] [label = above : 2] at (2) {};
    \node[vertex] [label = below: 3] at (3) {};
    \node[vertex] [label = right: 4] at (4) {};
    \node[vertex] [label = left: 5] at (5) {};
    %   \draw (0,0) arc (0:270:8mm);
    %   \draw (0,0) arc (0:315:1.75cm and 1cm); 
    
    \path
    (-2 , 3  ) coordinate () {} node[left]      {face6}
    (1.5, 4.5) coordinate () {} node[left]      {face1}
    (1.8, 2.5  ) coordinate () {} node[left]    {face2}
    (3, 1.5) coordinate () {} node[left]        {face3}
    (4.5, 2.5) coordinate () {} node[left]      {face4}
    (2.5, -0.7) coordinate () {} node[left]     {face5}
    ;
    
\end{tikzpicture}   
\\ \\ \\
 \begin{tikzpicture}[c/.style={circle,draw,inner sep=2pt}] 
    \path[nodes={text=teal}]  
    (0,0)   node[c] (v1) {} node[below left]    {$v_1$} 
    (15,0)  node[c] (v2) {} node[below right]   {$v_2$} 
    (10,1)  node[c] (v3) {} node[below]         {$v_3$} 
 %  (8,2)   node[c] (v3) {} node[below]         {$v_4$} 
    (7,8)   node[c] (v16){} node[above]         {$v_{16}$} ; 
    
    
    \draw (v1)--(v2)--(v3)--(v1); 
    \draw (v1) to[bend left=30] (v16) (v2) to[bend right] (v16) ; 
\end{tikzpicture}

Ergebnis wie dieses: