Extremal Cylinder Configurations I: Configuration Cm

Oleg Ogievetsky, Senya Shlosman

Research output: Contribution to journalArticlepeer-review


We study the path Γ = { C6,x∣ x∈ [0 , 1] } in the moduli space of configurations of six equal cylinders touching the unit sphere. Among the configurations C6,x is the record configuration Cm of Ogievetsky and Shlosman (Discrete Comput Geom 2019, https://doi.org/10.1007/s00454-019-00064-3). We show that Cm is a local sharp maximum of the distance function, so in particular the configuration Cm is not only unlockable but rigid. We show that if (1 + x) (1 + 3 x) / 3 is a rational number but not a square of a rational number, the configuration C6,x has some hidden symmetries, part of which we explain.

Original languageEnglish
Pages (from-to)140-164
Number of pages25
JournalDiscrete and Computational Geometry
Issue number1
Publication statusPublished - Jul 2021


  • Critical configuration
  • Integrability
  • Unlocking procedure


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