Abstract
Insight into the efficient filling of space in systems of binary spheres is explored using bipyramids consisting of 3</=n</=8 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 0.001</=R</=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>/=0.9473 and for 0.8493>/=R>/=0.7434. A topological instability eliminates compact packings for R</=0.1547. Pentagonal bipyramids cover a larger range in R than any other compact bipyramids studied.
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