The Postnikov system of a path-connected space X is a tower of spaces $...\longrightarrow X_{n+1}\longrightarrow X_{n}\longrightarrow ...\longrightarrow X_{1}\longrightarrow X_{0}$ with the following properties:

1) each map $X_{n+1}\longrightarrow X_{n}$ is a fibration.

2) $\pi_{k}(X_{n})=\pi_{k}(X)$ for $k \leqslant n$.

3) $\pi_{k}(X_{n})=0$ for $k > n$.

Every CW-complexes has such a Postnikov system, and it is unique up to homotopy. The space X can be reconstructed from the Postnikov system as its inverse limit.

If $X$ is the Bruhat-Tits tree of $PGL(2,F)$, where $F$ a locally compact non-archimidian fields. As a topological space $X$ is CW-complexe and then it posseses a postnikov system. We can construct a tower of graphs over $X$

$...\longrightarrow X_{n+1}\longrightarrow X_{n}\longrightarrow ...\longrightarrow X_{1}\longrightarrow X_{0}$

such that their invere limit is disjoint union of $X$ indexeces by the points of the board of $X$.

The set of vertex of $X_{n}$ is the set of geodesic path of length $n$ in $X$ and the set of edges is the set of geodesic path of length $n+$ in $X$.

My question is : Is this tower of graphs is Postinikov System for $X$. If it is not clear that this tower is Postnikov System or not, how we can construct a Postnikov system for $X$