Non-Crystalline Compact Packings of Hard Spheres of Two Sizes: Bipyramids and the Geometry of Common Neighbours (Preprint)

摘要

Insight into the efficient filling of space in systems of binary spheres is explored using bipyramids consisting of 3-to-8 n tetrahedra sharing a common pair of spheres. Compact packings are sought in bipyramids consisting of larger hard spheres of unit radius and smaller hard spheres of radius between .001 and 1. Seventy-seven distinct compact bipyramids are found. The number of distinct compact bipyramids increases with the number n of constituent tetrahedra. No compact bipyramids are found for R greater than 0.9473 and for R between 0.8493 and 0.7434. A topological instability eliminates compact packings for R less than 0.1547. Pentagonal bipyramids cover a larger range in R than any other compact bipyramids studied.