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De Loera, Hogan, Oliveros, and Yang (2021) explored how other simplicial complexes can emerge as nerve complexes for sufficiently large point sets. In this paper, we establish a connection between the theory of word-representable graphs and a method for encoding the 1-skeletons of simplicial complexes to generate nerve complexes. Specifically, we demonstrate that every triangle-free 2-word-representable graph can be realized as a nerve complex in the plane, given sufficiently many points. 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