My question is relative to a geometric interpretation of the $BN$-pairs that arise in Tits' theory of buildings. Here is a definition that comes from an article by G. Stroth (*Nonspherical spheres*).

$[\ldots]$

Let $\mathcal{P} = \{P_1, \ldots, P_n\}$ be a minimal parabolic system for a group $G$, $B=P_1 \cap \ldots \cap P_n$ the Borel subgroup. A subgroup $N$ of $G$ is called a Weyl group for $\mathcal{P}$ iff

1) $N= \langle x_1, \ldots, x_n \rangle, x_i \in P_i-B, x_i^2 \in B$.

2) $B \cap N$ is a normal subgroup of $N$.

3) $N \cap P_i = (B \cap N) \langle x_i \rangle , i = 1, \ldots, n$.

$[\ldots]$

If additionally we have

(A) $G = BNB$ and

(B) $BgBhB \subset (BgB) \cup (BghB)$ for all $g,h \in N$

then we have a $BN$-pair. Geometrically, the Weyl group $N$ is the stabilizer of an apartment $\Delta$ of the geometry $\Gamma$ defined from $\mathcal{P}$, and $B$ is the stabilizer of a chamber of $\Delta$. I am trying to get a clear geometric view of these objects.

Here is my question. What could be a geometric interpretation of condition (B)?