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I am trying to study (finite) spherical buildings from a very combinatorial point of view : Every rank 3 spherical building is a finite simplicial complex of dimension 3, so one can define its density ...

Let $\underline{w} = [s_1, s_2, \dots ,s_n]$ be a reduced expression in a Coxeter group $W$. Given $x$ in $W$ one can consider the set $\Pi(\underline{w},x)$ consisting of all subexpressions of $\...

Somewhere, I don't remember where, I saw a beautiful 3D figure of part a CAT(0) simplicial complex. I am thinking and hoping that this was some finite piece of an affine building of type A2, ...