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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
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: |
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| 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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