Extremal Cylinder Configurations II: Configuration O₆

Abstract

We study the octahedral configuration O₆ [Kuperberg] of six equal cylinders touching the unit sphere. We show that the configuration O₆ is a local sharp maximum of the distance function. Thus, it is not unlockable and, moreover, rigid.

Keywords:

• locally maximal configuration; rigid configuration; unlockable configuration; distance function; connected components

Additional information

Funding

Part of the work of S. S. has been carried out in the framework of the Labex Archimede (ANR-11-LABX-0033) and of the A*MIDEX project (ANR-11- IDEX-0001-02), funded by the Investissements d’Avenir French Government program managed by the French National Research Agency (ANR). Part of the work of S. S. has been carried out at IITP RAS. The support of Russian Foundation for Sciences (project No. 14-50-00150) is gratefully acknowledged by S. S. The work of O. O. was supported by the Program of Competitive Growth of Kazan Federal University and by the grant RFBR 17-01-00585.