Ogievetsky, Oleg; Shlosman, Senya Extremal cylinder configurations. II: Configuration \(O_6\). (English) Zbl 07566897 Exp. Math. 31, No. 2, 486-496 (2022). Summary: We study the octahedral configuration \(O_6\) [Kuperberg] of six equal cylinders touching the unit sphere. We show that the configuration \(O_6\) is a local sharp maximum of the distance function. Thus, it is not unlockable and, moreover, rigid. For Part I, see [O. Ogievetsky and S. Shlosman, Discrete Comput. Geom. 66, No. 1, 140–164 (2021; Zbl 1468.52012)]. Cited in 4 Documents MSC: 51-XX Geometry 30-XX Functions of a complex variable Keywords:locally maximal configuration; rigid configuration; unlockable configuration; distance function; connected components Citations:Zbl 1468.52012 Software:Mathematica PDFBibTeX XMLCite \textit{O. Ogievetsky} and \textit{S. Shlosman}, Exp. Math. 31, No. 2, 486--496 (2022; Zbl 07566897) Full Text: DOI arXiv References: [1] Conway, J. H.; Sloane, N. J. A., Sphere Packings, Lattices and Groups, 290 (2013), New York: Springer Science & Business Media, New York [2] Kuperberg, W. (1990) [3] Kuperberg, W., MathOverflow page [4] Kusner, R.; Kusner, W.; Lagarias, J. C.; Shlosman, S.; Ambrus, G.; Bárány, I.; Böröczky, K.; Fejes Tóth, G.; Pach, J., New Trends in Intuitive Geometry, Bolyai Society Mathematical Studies, 27, Configuration Spaces of Equal Spheres Touching a Given Sphere: The Twelve Spheres Problem (2018), Berlin, Heidelberg: Springer, Berlin, Heidelberg · Zbl 1411.52002 [5] [Ogievetsky and Shlosman 18] Ogievetsky, O. and Shlosman, S.. “Extremal Cylinder Configurations I: Configuration \(####\)” arXiv:1812.09543, 2018. · Zbl 1468.52012 [6] [Ogievetsky and Shlosman 19a] Ogievetsky, O. and Shlosman, S.. “The Six Cylinders Problem: \(####\)-Symmetry Approach.” Discrete & Computational Geometry (2019a), 1-20. · Zbl 1458.05041 [7] [Ogievetsky and Shlosman 19b] Ogievetsky, O. and Shlosman, S.. “Platonic Compounds of Cylinders.” arXiv:1904.02043, 2019b. · Zbl 1468.52013 [8] [Viro and Viro 06] Viro, J. and Viro, O.. “Configurations of Skew Lines.” arXiv preprint math/0611374, 2006. · Zbl 1131.14062 [9] Wolfram Research, Inc, Mathematica, Version 11.3 (2018), Champaign, IL: Wolfram Research, Inc, Champaign, IL This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.