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For each integer $k\ge 6$ and each finite graph $L$, we construct a Coxeter group $W$ and a non positively curved polygonal complex $A$ on which $W$ acts properly cocompactly, such that each polygon of $A$ has $k$ edges, and the link of each vertex of $A$ is isomorphic to $L$. If $L$ is a “generalized $m$-gon”, then $A$ is a Tits building modelled on a reflection group of the hyperbolic plane. We give a condition on $\mathrm{Aut}\left(L\right)$ for $\mathrm{Aut}\left(A\right)$ to be non enumerable (which is satisfied if $L$ is a thick classical generalized $m$-gon). On the other hand,...