Work

On Extreme Constant Width Bodies in $$\mathbb {R}^3$$

Year: 2025

Type: article

Abstract: We consider the family of constant width bodies in $$\mathbb {R}^3$$ 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 polyhedron is extreme. We also explain that each constant width body obtained by rotating a symmetric Reuleaux polygon about its line of symmetry is extreme. In addition, we conjecture a general characterization of all extreme constant width shapes.

Source: Discrete & Computational Geometry

DOI: 10.1007/s00454-025-00779-6

Author: Ryan Hynd

Institution: University of Pennsylvania

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: National Science Foundation