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More generally, when does $\\Gamma$ admit a finite-dimensional representation with infinite image over a commutative unital ring? If $X$ is the Bruhat--Tits building of a simple algebraic group over a local field and if $\\Gamma$ is an arithmetic lattice, then $\\Gamma$ is clearly linear. We prove that if $X$ is of type $\\widetilde A_2$, then the converse holds. 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