form of the encompassing disk and the disks themselves, is circular, that an optimal packing incorporating distorted rings emerges for these numbers of disks. The bottom panel of Fig. 14 is a diagram of the contact network for the backbone of the N = 40 optimal packing. FIG. 14: Diagrams [30] of contact networks for the N = 25 (a) and N = 40 (b) optimal packings, with point group symmetries D$_{5}$$_{h}$ and D$_{2}$$_{h}$ , respectively. The presence of these cavities about the central disk leads to an interesting counterintu- itive result. Suppose that in a binary liquid of nonoverlapping disks of unit diameter, one species of disk is endowed with an attractive square well potential. The potential of the “attractive” disks, present in the dilute limit in comparison to the “nonattractive” disks, acts on the centers of the “nonattractive” disks extending only to a distance just larger than any of the R$_{min}$ ( N ) presented in Figs. 12 or 13. If the depth (strength) of this square well were made arbitrarily large, then the result would seem paradoxical: unbounded attraction to the disks, in a minimal energy configuration, would eliminate contact with these disks. This effect in such a binary liquid of disks requires that the pair correlation function depicting the probability density of finding the centers of a given number of “nonattractive” disks a certain distance from the centers of “attractive” disks be zero from r = 0 to r = 24 (b) (a)