We investigated pseudo-cubic Cu2-xTe nanosheets using electron diffraction tomography and high-resolution HAADF-STEM imaging. The structure of this metastable nanomaterial, which has a strong localized surface plasmon resonance in the near-infrared region, was determined ab initio by 3D electron diffraction data recorded in low-dose nanobeam precession mode, using a new generation background-free single-electron detector. The presence of two different, crystallographically defined modulations creates a 3D connected vacancy channel system, which may account for the strong plasmonic response of this material. Moreover, a pervasive rotational twinning is observed for nanosheets as thin as 40 nm, resulting in a tetragonal pseudo-symmetry.