PreprintarXiv licencearXiv
A new family of constant width bodies obtained from Reuleaux polyhedra
Abstract
We give a construction of a body of constant width from a unit Reuleaux polyhedron that preserves all its symmetries. As opposed to the Meissner surgery, our construction modifies both edges of each dual pair and requires no choice between them. For the Reuleaux tetrahedron it recovers a previously known body of constant width with six elliptic edges and tetrahedral symmetry.
Related
- Geometric Realizations with Strong Self-Duality Part II: Diameter Graphs, Reuleaux Polyhedra, and Thrackles
- Approximation algorithm for mixed volumes of a constant number of convex bodies
- Optimal stability of Pál's isominwidth inequality for ball convex bodies in planes of constant curvature
- An Infinite Family of Apéry-like Recurrences for Euler's Constant
- A family of Hurwitz polynomial vector fields in ℝ3 having non-constant periodic orbits
BibTeX
@misc{mercadoflores2026family,
title = {{A new family of constant width bodies obtained from Reuleaux polyhedra}},
author = {Marcela G. Mercado-Flores and Edgardo Roldán-Pensado},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16997},
eprint = {2610.16997},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16997},
}
RIS
TY - UNPB
TI - A new family of constant width bodies obtained from Reuleaux polyhedra
AU - Marcela G. Mercado-Flores
AU - Edgardo Roldán-Pensado
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16997
UR - https://arxiv.org/abs/2610.16997
AB - We give a construction of a body of constant width from a unit Reuleaux polyhedron that preserves all its symmetries. As opposed to the Meissner surgery, our construction modifies both edges of each dual pair and requires no choice between them. For the Reuleaux tetrahedron it recovers a previously known body of constant width with six elliptic edges and tetrahedral symmetry.
ER -