the pair module in $\tau_6$. Lastly, the most populated cluster for $N=8$, $\tau_8$ (58.4%), is formed by a backbone of four sites as in $\tau_6$ and $\tau_7$, with the remaining four sites organized into two pairs. At an increase of the granularity parameter to the value $p=1.7$, this cluster breaks into two smaller clusters that differ only in the location of the pairs: the more populated cluster $\tau_8^a$ (47.1%) has the two pairs on the same side of the backbone, where they form a triangle with the two intermediate sites of the backbone (Fig. \[fig:N4cl12\], fifth row right); the two pairs of the smaller cluster $\tau_8^b$ (10.3%) are instead diametrically opposed with respect to the backbone axis.

Backbones composed of five sites emerge for $N=7$. The most populated cluster $\pi_7$ (53,1%, fourth row of Fig. \[fig:N4cl12\], on the left), is in fact formed by five sites organized in a backbone geometry similar to $\pi_a$ with an additional pair similar to the case of $\tau_6$.

With this choice for the granularity parameters, the remaining clusters are less well defined. The second cluster $v_6$ for $N=6$ (24.8%), is composed of heterogeneous structures which are hard to reconduct to a single structural motif. 