On 3-dimensional hyperbolic Coxeter pyramids
Metric Geometry
2015-03-03 v1
Abstract
After classifying 3-dimensional hyperbolic Coxeter pyramids by means of elementary plane geometry, we calculate growth functions of corresponding Coxeter groups by using Steinberg formula and conclude that growth rates of them are always Perron numbers. We also calculate hyperbolic volumes of them and compare volumes with their growth rates. Finally we consider a geometric ordering of Coxeter pyramids comparable with their growth rates.
Keywords
Cite
@article{arxiv.1503.00583,
title = {On 3-dimensional hyperbolic Coxeter pyramids},
author = {Yohei Komori and Yuriko Umemoto},
journal= {arXiv preprint arXiv:1503.00583},
year = {2015}
}
Comments
15 pages, 9 figures