English

The Six Cylinders Problem: $\mathbb{D}_{3}$-symmetry Approach

Metric Geometry 2019-05-13 v2

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,r, all touching the unit ball in R3.\mathbb{R}^{3}. We find a configuration with r=18(3+33)1.093070331 . r=\frac{1}{8}\left( 3+\sqrt{33}\right) \approx1.093070331\ . We believe that this value is the maximal possible.

Keywords

Cite

@article{arxiv.1805.09833,
  title  = {The Six Cylinders Problem: $\mathbb{D}_{3}$-symmetry Approach},
  author = {Oleg Ogievetsky and Senya Shlosman},
  journal= {arXiv preprint arXiv:1805.09833},
  year   = {2019}
}
R2 v1 2026-06-23T02:07:35.660Z