I. INTRODUCTION A packing is defined as a set of nonoverlapping objects arranged in a space of given di- mension. Packings of identical nonoverlapping spheres in d -dimensional Euclidean space$_{R}$ d have been employed in condensed matter and materials physics as models for the structures of a diverse range of substances from crystals and colloids to liquids, amorphous solids and glasses [1–3]. In structural biology, molecular dynamics simulations of interactions between large numbers of molecules employ chains of nonoverlapping spheres as models for various biological structures such as proteins and lipids [4–6]. In part due to the ability of these conceptually simple models to describe many of the fundamental characteristics of more complex substances, understanding the properties of sphere packings has also long been an area of interest in mathematics (for example, see [7]). However, solving even some of the most basic of mathematical problems has proved challenging. For example, a proof of the Kepler conjecture, a proposition stating that the face-centered cubic lattice is the densest possible arrangement of spheres for d = 3, has only recently emerged [8]. Furthermore, the kissing number K$_{d}$ , or number of identical d -dimensional nonoverlapping spheres that can simultaneously be in contact with (kiss) a central sphere, was until recently only known rigorously for d = 1 − 3, 8 and 24 [9], though Musin [10] has now proved the d = 4 case ( K$_{4}$ = 24). One sphere packing problem that has not been generally addressed for an arbitrary num- ber of spheres is that of finding the maximally dense (optimal) packing(s) of N identical d -dimensional nonoverlapping spheres near (local to) an additional fixed central sphere such that the greatest radius R from any of the surrounding spheres’ centers to the center of the fixed sphere is minimized. This problem is called the densest local packing (DLP) problem [11]. There is a single minimized greatest radius, denoted by R$_{min}$ ( N ), for each N in the DLP problem in R $^{d}$, though generally for each N there may be multiple distinct packings that achieve this radius. Figure 1 depicts a conjectured optimal packing, belonging to point group D$_{5}$$_{h}$ [12], for the DLP problem for N = 15, d = 2, with R$_{min}$ (15) = 1 . 873123 ... [13]. In various limits, the densest local packing problem encompasses both the kissing number and (infinite) sphere packing problems. The former is a special case of the DLP problem in that K$_{d}$ is equal to the greatest N for which R$_{min}$ ( N ) = 1, and the latter is equivalent to the DLP problem in the limit that N → ∞ . The equivalence of the latter problem may be 2