two clusters $\tau_a$ and $\tau_b$ (first row of Fig. \[fig:N4cl12\]); they represent 63.1% and 36.9% of the total population, respectively. In both cases the four sites are equidistant from each other. However, in the latter case, the two intermediate sites are arranged along the input-output axis while in the former case they are slightly offset.

For $N=5$, the situation is similar, but there is an extra intermediate site. Two clusters, named $\pi_a$ and $\pi_b$ (second row of Fig. \[fig:N4cl12\]), represent 83.5% and 15.8% of the total population (the remaining 0.7% is noise). In this case there is a slight deviation from an equidistant distribution of the inter-site distances. In the cluster $\pi_b$ the 3 intermediate sites are aligned along an axis which is rotated with respect to the in-out one; in $\pi_a$ these three sites form a triangle.

![image](IPR_5.pdf){width="99.00000%"}

Interestingly, the structures found for $N=4$ and $N=5$ constitute the building blocks for the higher dimensional cases (see Supp. Fig. \[fig:supp:VMDrepr1\],\[fig:supp:VMDrepr2\],\[fig:supp:VMDrepr3\]). In fact, systems with $N>5$ present a higher degree of heterogeneity and a prototypical modular structure. The first module is comprised by four/five sites approximately lined up along the in-out axis; this defines a structural backbone. In all cases this 