The Six Cylinders Problem: ${\mathbb{D}}_3$-symmetry Approach

Abstract

Motivated by a question of W. Kuperberg, we study the 18-dimensional manifold of configurations of 6 non-intersecting infinite cylinders of radius $r,$ all touching the unit ball in ${\mathbb{R}}^3.$ We find a configuration with \[ r=\frac{1}{8}\left( 3+\sqrt{33}\right) \approx1.093070331\ .\] We believe that this value is the maximal possible.

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