conclude that ${\partial_{\mathcal{A}}}X$ is a spherical building.

\[Def\_germ\] Two Weyl simplices $S$ and $S'$ *share the same germ* if both are based at the same vertex and if $S\cap S'$ is a neighborhood of $x$ in $S$ and in $S'$.

It is easy to see that this is an equivalence relation on the set of Weyl simplices based at a given vertex. The equivalence class of an $x$-based Weyl simplex $S$ is denoted by $\Delta_x S$ and is called the *germ of $S$ at $x$*.

The germs of Weyl simplices at a special vertex $x$ are partially ordered by inclusion: $\Delta_x S_1$ is contained in $\Delta_xS_2$ if there exist $x$-based representatives $S'_1, S'_2$ contained in a common apartment such that $S_1'$ is a face of $S_2'$. Let $\Delta_xX$ be the set of all germs of Weyl simplices based at $x$.

Recall that a germ $\mu$ of a Weyl chamber $S$ at $x$ is *contained in a set $Y$* if there exists $\varepsilon\in\Lambda^{+}$ such that $S\cap B_\varepsilon(x)$ is contained in $Y$.

\[Prop\_tec16\] Let $(X, {\mathcal{A}})$ be an affine building and $c$ a chamber in ${\partial_{\mathcal{A}}}X$. Let $S$ be a Weyl chamber in $X$ based at $x$. Then there exists an apartment 