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Packing twelve spherical caps to maximize tangencies

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Flatley, Lisa, Tarasov, Alexey, Taylor, Martin and Theil, Florian (2013) Packing twelve spherical caps to maximize tangencies. Journal of Computational and Applied Mathematics, volume 254 . pp. 220-225. doi:10.1016/j.cam.2013.03.036

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Official URL: http://dx.doi.org/10.1016/j.cam.2013.03.036

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Abstract

The maximum number of non-overlapping unit spheres in R3 that can simultaneously touch another unit sphere is given by the kissing number, k(3)=12. Here, we present a proof that the maximum number of tangencies in any kissing configuration is 24 and that, up to isomorphism, there are only two configurations for which this maximum is achieved. The result is motivated by a three-dimensional crystallization problem.

Item Type: Journal Article
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Journal of Computational and Applied Mathematics
Publisher: Elseivier Science BV
ISSN: 0377-0427
Official Date: 2013
Dates:
DateEvent
2013Published
Volume: volume 254
Page Range: pp. 220-225
DOI: 10.1016/j.cam.2013.03.036
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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