The minimal covolume right-angled Coxeter group in hyperbolic 3-space
Geometric Topology
2025-09-12 v1
Abstract
We prove that among all right-angled Coxeter groups in hyperbolic 3-space, the group generated by reflections in the faces of a right-angled triangular bipyramid with three ideal and two finite vertices has the smallest covolume. The group is arithmetic and its covolume equals Catalan's constant G = 0.915965....
Keywords
Cite
@article{arxiv.2509.09261,
title = {The minimal covolume right-angled Coxeter group in hyperbolic 3-space},
author = {A. Egorov and A. Vesnin},
journal= {arXiv preprint arXiv:2509.09261},
year = {2025}
}
Comments
17 pages, 11 figures