New bounds on the number of unit spheres that can touch a unit sphere in n dimensions

A. M. Odlyzko; N. J.A. Sloane

doi:10.1016/0097-3165(79)90074-8

New bounds on the number of unit spheres that can touch a unit sphere in n dimensions

A. M. Odlyzko
, N. J.A. Sloane

School of Mathematics

Research output: Contribution to journal › Article › peer-review

131 Scopus citations

Abstract

New upper bounds are given for the maximum number, τ_n, of nonoverlapping unit spheres that can touch a unit sphere in n-dimensional Euclidean space, for n≤24. In particular it is shown that τ₈ = 240 and τ₂₄ = 196560.

Original language	English (US)
Pages (from-to)	210-214
Number of pages	5
Journal	Journal of Combinatorial Theory, Series A
Volume	26
Issue number	2
DOIs	https://doi.org/10.1016/0097-3165(79)90074-8
State	Published - Mar 1979

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title = "New bounds on the number of unit spheres that can touch a unit sphere in n dimensions",

abstract = "New upper bounds are given for the maximum number, τn, of nonoverlapping unit spheres that can touch a unit sphere in n-dimensional Euclidean space, for n≤24. In particular it is shown that τ8 = 240 and τ24 = 196560.",

author = "Odlyzko, \{A. M.\} and Sloane, \{N. J.A.\}",

year = "1979",

month = mar,

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journal = "Journal of Combinatorial Theory, Series A",

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T1 - New bounds on the number of unit spheres that can touch a unit sphere in n dimensions

AU - Odlyzko, A. M.

AU - Sloane, N. J.A.

PY - 1979/3

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N2 - New upper bounds are given for the maximum number, τn, of nonoverlapping unit spheres that can touch a unit sphere in n-dimensional Euclidean space, for n≤24. In particular it is shown that τ8 = 240 and τ24 = 196560.

AB - New upper bounds are given for the maximum number, τn, of nonoverlapping unit spheres that can touch a unit sphere in n-dimensional Euclidean space, for n≤24. In particular it is shown that τ8 = 240 and τ24 = 196560.

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UR - https://www.scopus.com/pages/publications/0001179224#tab=citedBy

U2 - 10.1016/0097-3165(79)90074-8

DO - 10.1016/0097-3165(79)90074-8

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JO - Journal of Combinatorial Theory, Series A

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IS - 2

ER -

New bounds on the number of unit spheres that can touch a unit sphere in n dimensions

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