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Let $\mathfrak{g}$ be a hyperbolic Kac-Moody algebra of rank $2$. We give apolyhedral realization of the crystal basis for the extremal weight module ofextremal weight $\lambda$, where $\lambda$ is an integral weight whose Weylgroup orbit has neither a dominant integral weight nor an antidominant integralweight.

Polyhedral realization of the crystal bases for extremal weight modules over quantized hyperbolic Kac-Moody algebras of rank 2