A volume formula for Reuleaux polyhedra
Metric Geometry
2026-01-21 v1
Abstract
A ball polyhedron is a finite intersection of congruent balls in . These shapes arise in various contexts in discrete and convex geometry. We focus on Reuleaux polyhedra, the subclass of ball polyhedra whose centers and vertices coincide. Building on Bogosel's recent work on the volume of Meissner polyhedra, we derive a formula for the volume of Reuleaux polyhedra in terms of their edges.
Cite
@article{arxiv.2601.11756,
title = {A volume formula for Reuleaux polyhedra},
author = {Ryan Hynd},
journal= {arXiv preprint arXiv:2601.11756},
year = {2026}
}