The commensurate charge-density-wave phase of the prototypical transition metal dichalcogenide -TaS is investigated by temperature- and polarization-dependent infrared spectroscopy, revealing distinct charge dynamics parallel and perpendicular to the layers. Supported by density-functional-theory calculations, we show that the in-plane electronic structure in the low-temperature commensurate phase is reconstructed by the distortion of the Ta layers. In contrast, the out-of-plane response is governed by a quasi-one-dimensional, Peierls-like dimerization of the two-dimensional star-of-David layers. Our results identify this dimerization as the dominant mechanism of the metal-to-insulator transition in both directions, ruling out a significant role of electronic correlations.

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