The Six Cylinders Problem: D <inf>3</inf> -Symmetry Approach

Abstract

© 2019, Springer Science+Business Media, LLC, part of Springer Nature. Motivated by a question of W. Kuperberg, we study the 18-dimensional manifold of configurations of six non-intersecting infinite cylinders of radius r, all touching the unit ball in R 3 . We find a configuration with r=18(3+33)≈1.093070331.We believe that this value is the maximum possible.