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

Mathematics

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

110 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

Access

10.1016/0097-3165(79)90074-8

Cite this

@article{5d35c1d0ac26462f9a471af0ae54c20e,

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,

doi = "10.1016/0097-3165(79)90074-8",

language = "English (US)",

volume = "26",

pages = "210--214",

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

issn = "0097-3165",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

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

Y1 - 1979/3

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.

UR - http://www.scopus.com/inward/record.url?scp=0001179224&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001179224&partnerID=8YFLogxK

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

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

M3 - Article

AN - SCOPUS:0001179224

VL - 26

SP - 210

EP - 214

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 2

ER -

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

Abstract

Access

Other files and links

Fingerprint

Cite this