\documentclass{article} % say
\usepackage{tikz}
\begin{document}
%We are working on
\begin{tikzpicture}
\usetikzlibrary{patterns}

% traits horizontaux


\node (A) at (0,0) [coordinate] {} ;
\node [below left] at (A) {A} ;
\node (B) at (8.5,4) [coordinate] {} ;
\node [right] at (B) {B} ;
\node (C) at (1,11.5) [coordinate] {} ;
\node [above right] at (C) {C} ;
\node (D) at (-4,4) [coordinate] {} ;
\node [above left] at (D) {$\pi_0$} ;
\node [below left] at (D) {D} ;
\node (E) at (-2,2) [coordinate] {} ;
\node [below left] at (E) {E} ;
\node (F) at (2,2.5) [coordinate] {} ;
\node [right] at (F) {F} ;
\node (G) at (3,4) [coordinate] {} ;
\node [above right] at (G) {G} ;
\node (H) at (2,6.5) [coordinate] {} ;
\node [right] at (H) {H} ;
\node (I) at (-1.5,7.75) [coordinate] {} ;
\node [above left] at (I) {I} ;
\node (J) at (-1.5,5) [coordinate] {} ;
\node [above left] at (J) {J} ;
\node (K) at (-1.628,4) [coordinate] {} ;
%\node [above left] at (K) {K} ;
\node (L) at (1.5,5) [coordinate] {} ;
\node [above right] at (L) {\bf L} ;

\draw (B) -- (C) -- (D) -- (E) -- (A) -- (B);

\draw (A) -- (C);

\draw [dashed] (D) -- (K);
\draw [dashed] (G) -- (B);

\draw [line width=1pt,densely dashed] (E) -- (F) -- (L) -- (E) -- (J) -- (L) -- (I) -- (H) -- (L) -- (G) -- (F);
\draw [line width=1pt,densely dashed] (I) -- (J);
\draw [line width=1pt,densely dashed] (G) -- (H);

\filldraw[color=lightgray,pattern=horizontal lines] (I) -- (J) -- (L) %-- (H)
;
\filldraw[color=lightgray,pattern=vertical lines] (I) -- (H) -- (L) %-- (H)
;
\filldraw[color=lightgray,pattern=north east lines] (F) -- (L) -- (H) -- (G);
\filldraw[color=lightgray,pattern=north west lines] (E) -- (J) -- (L) -- (F);
\filldraw[color=lightgray,pattern=dots] (E) -- (J) -- (I) -- (D);

\draw (-0.7,9.5) node{$\pi_1^1$};
\draw (-1.5,1) node{$\pi_1^2$};
\draw (5,4.3) node{$\pi_1^3$};
\draw (3.6,7) node{$\pi$};
\draw (-4,-2.3) node{$\tau$};


\end{tikzpicture}
\end{document}

