\documentclass[12pt]{article}
\usepackage{pgfplots}


\begin{document}

%
%\begin{figure}[!ht]
\begin{tikzpicture}
\begin{axis}[view/h=120,xlabel=$x$,ylabel=$y$]

\addplot3[
opacity=1,
table/row sep=\\,
patch,
% patch type=polygon,
shader=interp,
% line width=1pt,
% vertex count=5,
% patch table with point meta={%
patch table={%
% pt1 pt2 pt3 pt4 pt5 cdata
0 1 7 \\
1 6 5 \\
1 5 4 \\
1 4 7 \\
7 4 2 \\
2 4 3 \\
0 7 2 \\
0 8 1 \\
1 8 6 \\
6 8 5 \\
5 8 4 \\
4 8 3 \\
3 8 2 \\
2 8 0 \\
}]
table [point meta=\thisrow{c}]{
x y z c \\
0 2 0 0 \\%0
2 2 0 0 \\%1
0 1 3 3 \\%2
0 0 3 3 \\%3
1 0 3 3 \\%4
2 0 2 2 \\%5
2 0 0 0 \\%6
1 1 3 10 \\%7
0 0 0 10 \\%8
1 0 3 0 \\%9=4 copy
1 1 2 0 \\%10=7 copy
};

% replicate the vertex list to show \coordindex: 
\addplot3[only marks,nodes near coords=\coordindex]
table[row sep=\\] {
0 2 0\\ 2 2 0\\ 0 1 3\\ 0 0 3\\
1 0 3\\ 2 0 2\\ 2 0 0\\ 1 1 2\\ 0 0 0\\
};

\end{axis}
\end{tikzpicture}
%\end{figure}

\end{document}