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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

An algorithm for generating the sphere coordinates in a three-dimensional osculatory packing


Author: David W. Boyd
Journal: Math. Comp. 27 (1973), 369-377
MSC: Primary 52A45; Secondary 52-04
MathSciNet review: 0338937
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Abstract: This paper develops an efficient algorithm which generates the pentaspherical coordinates of the spheres in an osculatory packing of the three-dimensional unit sphere. The algorithm has a tree-like structure and is easily modified so that, given a prescribed bound, it counts the number of spheres in the packing whose curvatures are less than this bound. The algorithm has been used to produce heuristic estimates of the exponent M of the packing, and these indicate that M is approximately 2.42.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1973-0338937-6
PII: S 0025-5718(1973)0338937-6
Keywords: Sphere packing, osculatory packing, exponent of packing, algorithm, computer study
Article copyright: © Copyright 1973 American Mathematical Society