On compact hyperbolic Coxeter d-polytopes with d+4 facets
Metric Geometry
2019-10-25 v2 Group Theory
Abstract
We show that there is no compact hyperbolic Coxeter d-polytope with d+4 facets for d>7. This bound is sharp: examples of such polytopes up to dimension 7 were found by Bugaenko (1984). We also show that in dimension d=7 the polytope with 11 facets is unique.
Keywords
Cite
@article{arxiv.math/0510238,
title = {On compact hyperbolic Coxeter d-polytopes with d+4 facets},
author = {Anna Felikson and Pavel Tumarkin},
journal= {arXiv preprint arXiv:math/0510238},
year = {2019}
}
Comments
v2: the paper is rewritten. A new section added in which 7-dimensional polytopes are classified. 43 pages, a lot of figures