  The combinatorial invariance conjecture (due independently to G. Lusztig and
M. Dyer) predicts that if $[x,y]$ and $[x',y']$ are isomorphic Bruhat posets
(of possibly different Coxeter systems), then the corresponding Kazhdan-Lusztig
polynomials are equal, that is, $P_{x,y}(q)=P_{x',y'}(q)$. We prove this
conjecture for the affine Weyl group of type $\widetilde{A}_2$. This is the
first infinite group with non-trivial Kazhdan-Lusztig polynomials where the
conjecture is proved.
