  The transition metal dichalcogenide 1$T$-TiSe$_2$ is a quasi-two-dimensional
layered material undergoing a commensurate 2 $\times$ 2 $\times$ 2 charge
density wave (CDW) transition with a weak periodic lattice distortion (PLD)
below $\approx$ 200 K. Scanning tunneling microscopy (STM) combined with
intentionally introduced interstitial Ti atoms allows to go beyond the usual
spatial resolution of STM and to intimately probe the three-dimensional
character of the PLD. Furthermore, the inversion-symmetric, achiral nature of
the CDW in the $z$-direction is revealed, contradicting the claimed existence
of helical CDW stacking and associated chiral order. This study paves the way
to a simultaneous real-space probing of both charge and structural
reconstructions in CDW compounds.
