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arXiv · 2501.16940

On extreme constant width bodies in $\mathbb{R}^3$

Ryan Hynd
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Abstract

We consider the family of constant width bodies in $\mathbb{R}^3$ which is convex under Minkowski addition. Extreme shapes cannot be expressed as a nontrivial convex combination of other constant width bodies. We show that each Meissner polyhedra is extreme. We also explain that each constant width body obtained by rotating a symmetric Reuleaux polygon about its axis of symmetry is extreme. In addition, we conjecture a general characterization of all extreme constant width shapes.

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Ryan Hynd. 2025-01-28. On extreme constant width bodies in $\mathbb{R}^3$. https://arxiv.org/abs/2501.16940

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