module is compatible with either $\tau_a$/$\tau_b$ or $\pi_a$/$\pi_b$. The second module is essentially formed by the remaining two to four sites, organized in tightly packed *pairs* or *triplets*. Backbone sites are approximately equally spaced between input and output with typical inter-site distances of around $0.50-0.60 \ r_0$, depending on the specific case. Pair/triplet sites instead are always very close to each other with a inter-site distance of around $0.25 \ r_0$, depending on the particular organization. It is worth noting that the backbone arrangement of all mentioned systems is symmetric under input output inversion [@Mostarda2013; @Walschaers2013].

The organization of $\tau_b$ constitutes the backbone of the most populated cluster of $N=6$, $\tau_6$ (75.1%, third row of Fig. \[fig:N4cl12\]). In this cluster, we identify a pair whose position is less well defined than the position of the backbone sites. A backbone of four sites that resembles $\tau_b$ is present also in the second cluster for $N=7$, $\tau_7$ (46.9%, fourth row of Fig. \[fig:N4cl12\], on the right), where the remaining three sites lie close together at comparable reciprocal distances, [*i.e.*]{} they form a *triplet*. This triplet is located more heterogeneously than the intermediate sites, in a region comparable to the one occupied by 