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arXiv · 2610.26940

Littlewood's mutually touching cylinders: the maximum is seven

Ivan Matić·Radoš Radoičić·Andreas Spomer
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Abstract

We give a computer-assisted proof that eight congruent infinite circular cylinders in $\mathbb{R}^3$ cannot touch pairwise. Since seven such cylinders exist, the maximum number of congruent mutually touching infinite cylinders is seven. This answers a question of Littlewood from 1968.

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Ivan Matić, Radoš Radoičić, Andreas Spomer. 2026-10-18. Littlewood's mutually touching cylinders: the maximum is seven. https://arxiv.org/abs/2610.26940

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