Configuration spaces of equal spheres touching a given sphere: The twelve spheres problem

Rob Kusner, Wöden Kusner, Jeffrey C. Lagarias, Senya Shlosman

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in Buch/BerichtForschungBegutachtung

Abstract

The problem of twelve spheres is to understand, as a function of r ϵ (0,rmax(12)], the configuration space of 12 non-overlapping equal spheres of radius r touching a central unit sphere. It considers to what extent, and in what fashion, touching spheres can be varied, subject to the constraint of always touching the central sphere. Such constrained motion problems are of interest in physics and materials science, and the problem involves topology and geometry. This paper reviews the history of work on this problem, presents some new results, and formulates some conjectures. It also presents general results on configuration spaces of N spheres of radius r touching a central unit sphere, with emphasis on 3 ≤ N ≤ 14. The problem of determining the maximal radius rmax(N) is a version of the Tammes problem, to which László Fejes Tóth made significant contributions.

Originalspracheenglisch
TitelBolyai Society Mathematical Studies
Herausgeber (Verlag)Springer Berlin - Heidelberg
Seiten219-277
Seitenumfang59
DOIs
PublikationsstatusVeröffentlicht - 1 Jan 2018

Publikationsreihe

NameBolyai Society Mathematical Studies
Band27
ISSN (Print)1217-4696

Schlagwörter

    ASJC Scopus subject areas

    • !!Computational Theory and Mathematics
    • Angewandte Mathematik

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  • Dieses zitieren

    Kusner, R., Kusner, W., Lagarias, J. C., & Shlosman, S. (2018). Configuration spaces of equal spheres touching a given sphere: The twelve spheres problem. in Bolyai Society Mathematical Studies (S. 219-277). (Bolyai Society Mathematical Studies; Band 27). Springer Berlin - Heidelberg. https://doi.org/10.1007/978-3-662-57413-3_10