  Let $\Gamma$ be a group of type rotating automorphisms of a building $\cB$ of
type $\widetilde A_2$, and suppose that $\Gamma$ acts freely and transitively
on the vertex set of $\cB$. The apartments of $\cB$ are tiled by triangles,
labelled according to $\Gamma$-orbits. Associated with these tilings there is a
natural subshift of finite type, which is shown to be irreducible. The key
element in the proof is a combinatorial result about finite projective planes.
