Regular Totally Separable Sphere Packings

2015/06/06 by Reid, Samuel
#FOS: Mathematics #Metric Geometry (math.MG) #Primary 52B20 #Secondary 14H52

paper · doi:10.48550/arxiv.1506.04171

Abstract

The topic of totally separable sphere packings is surveyed with a focus on regular constructions, uniform tilings, and contact number problems. An enumeration of all regular totally separable sphere packings in ℝ², ℝ³, and ℝ⁴ which are based on convex uniform tessellations, honeycombs, and tetracombs, respectively, is presented, as well as a construction of a family of regular totally separable sphere packings in ℝ^d that is not based on a convex uniform d-honeycomb for d ≥ 3.

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