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Ordering of the two incommensurate charge density waves (CDW), $\mathbf{q_1}$ = (0.0, 0.243, 0.0) and $\mathbf{q_2}$ = (0.5, 0.263,0.5) in the quasi-one-dimensional NbSe$_3$ structure is studied by means of low temperature scanning tunneling microscopy. Larger (100) van der Waals surfaces are analyzed using one-dimensional Fourier transforms along the three types of trigonal prismatic columns, running parallel to the monoclinic $\mathbf{b_0}$ direction. The procedure enables unambiguous differentiation between both CDWs modulating individual columns. In addition, it allows a quantitative comparison of modulation amplitudes along different columns of the same type and, in case of sufficiently large images, also along individual columns. It is confirmed that each CDW modulates both type-III and type-I columns with the narrowest isosceles bases. As a consequence beating is observed between the two slightly different modes. The bridging type-II columns appear not to be modulated. On a large scale the modulation amplitudes along individual columns vary, suggesting formation of CDW nanodomains. The possibility of interchanging both CDWs along columns forming symmetry-related pairs results in a charge difference, which might be the possible origin of CDW sliding.

The basic and the charge density wave (CDW) structures of the monoclinic $NbS_3-II$ polymorph were studied by synchrotron x-ray diffraction, ab-initio calculation, simulation of electron diffraction patterns and by atomic-resolution transmission electron and low-temperature scanning tunneling microscopies. It is shown that the basic structure belongs to the space group $P2_1/m$ and is described with a unit cell, formed of four pairs of symmetry-related trigonal prismatic (TP) columns ($a_0$ = 0.96509(8) nm, $b_0$ = 0.33459(2) nm, $c_0$ = 1.9850(1) nm, $\beta_0$ = 110.695(4) deg), with all Nb and S atoms in $2e$ special positions. The two CDWs, with $\vec{q_1}$ = (0, 0.298,0) and $\vec{q_2}$ = (0, 0.352, 0), form their own modulation unit cells ($a_m$ = $2a_0$, $b_m$ = $b_0/q_{jb}$, $c_m$ = $c_0$, $\beta_m$ = $\beta_0$) and are ordered pairwise along adjacent isosceles TP columns. The symmetries of both $\vec{q_j}$ modes belong to the space group $Cm$ and are related according to the $2a$ special positions. If considered as long-period commensurate, the entire modulated structure with both CDWs included is best described with an enlarged unit cell ($a$ = $2a_0$, $b$ = $37b_0$, $c$ = $c_0$, $\beta$ = $\beta_0$), with all Nb and S atoms in $1a$ positions of the space group $P1$., Comment: v2.Minor changes to figures and text