Pairwise touching cylinders: existence for eight unit cylinders

Determine whether there exists a configuration of eight infinite circular cylinders of unit radius in ℝ^3 such that every pair of cylinders touches; either construct such a configuration or prove impossibility.

Background

The mutually touching cylinders problem explores geometric constraints of lines (axes) at fixed distance equal to twice the radius. Existence has been proved for seven unit cylinders; dimensional counting suggests difficulty for eight.

Resolving n = 8 would close a natural threshold case in this geometric extremal problem.

References

The question for $8$ cylinders remains open but it is likely that $7$ is the optimum based on numerical calculations and dimensional considerations.

— Mathematical exploration and discovery at scale  (2511.02864 - Georgiev et al., 3 Nov 2025) in Subsection “Pairwise touching cylinders” (Section 4.26)