\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usetikzlibrary{shapes, calc, shapes,snakes} 
\usepackage{amsmath,amssymb}

\begin{document}
\begin{preview}
\begin{tikzpicture}[thick]


    % Draw the triangle
    \fill[fill=gray!40]  (0, 0) coordinate (A) 
        -- (5,0) coordinate (B) 
        -- (0,2) coordinate (C) -- cycle;

    \fill[fill=blue!40]  (B)
        -- (C)
        -- (2,2) coordinate (D)
        -- (5,2) coordinate (E) -- cycle;

    \fill[fill=red!40]  (C)
        -- (D)
        -- (3,5) coordinate (G)
        -- (0,5) coordinate (F);

    \fill[fill=green!40]  (D)
        -- (E)
        -- (5,5) coordinate (H)
        -- (G);


    \fill[fill=green!40]  (6,1) coordinate (I)
        -- (9,1) coordinate (J)
        -- (9,2.9) coordinate (O)
        -- (6,4) coordinate (L);

    \fill[fill=gray!40]  (J)
        -- (14,1) coordinate (K)
        -- (O);

    \fill[fill=blue!40]  (L)
        -- (11,2.14) coordinate (P)
        -- (11,4) coordinate (M);

    \fill[fill=red!40]  (M)
        -- (14,4) coordinate (N)
        -- (K)
        -- (P);

    % Draw edge text
    \node (a) at ($(A)!0.5!(B)$) [below] {$f_n$};
    \node (b) at ($(A)!0.5!(C)$) [left] {$f_{n-2}$};
    \node (c) at ($(C)!0.5!(F)$) [left] {$f_{n-1}$};
    \node (d) at ($(C)!0.5!(D)$) [above] {$f_{n-2}$};
    \node (e) at ($(D)!0.5!(E)$) [above] {$f_{n-1}$};
    \node (f) at ($(F)!0.5!(G)$) [above] {$f_{n-1}$};
    \node (g) at ($(G)!0.5!(H)$) [above] {$f_{n-2}$};

    \node (h) at ($(N)!0.5!(K)$) [right] {$f_{n-1}$};
    \node (i) at ($(I)!0.5!(J)$) [below] {$f_{n-1}$};
    \node (j) at ($(J)!0.5!(K)$) [below] {$f_{n}$};

\draw [
    thick,
    decoration={
        brace,
        mirror,
        raise=0.5cm
    },
    decorate
] (I) -- (K) 
node [pos=0.5,anchor=north,yshift=-0.55cm] {$f_{n+1}$}; 

\end{tikzpicture}
\end{preview}
\end{document}
