Connelly's conjecture on optimality of triangulated disc packings

Let a finite set of discs be given. A packing is triangulated saturated if it is both triangulated and saturated, meaning that its contact structure is a triangulation and no further disc can be added without overlap. Connelly's conjecture. If the finite set of discs allows a triangulated saturated packing, then the density of packings by these discs is maximized on a triangulated packing.

This conjecture is motivated by the fact that, for the nine known binary radii admitting triangulated packings using both disc sizes, the density is maximized by such a packing. Its status is not resolved in the supplied source context.