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Essential hyperbolic Coxeter polytopes

Felikson, A.; Tumarkin, P.

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Abstract

We introduce a notion of an essential hyperbolic Coxeter polytope as a polytope which fits some minimality conditions. The problem of classification of hyperbolic reflection groups can be easily reduced to classification of essential Coxeter polytopes. We determine a potentially large combinatorial class of polytopes containing, in particular, all the compact hyperbolic Coxeter polytopes of dimension at least 6 which are known to be essential, and prove that this class contains finitely many polytopes only. We also construct an effective algorithm of classifying polytopes from this class, realize it in the four-dimensional case, and formulate a conjecture on finiteness of the number of essential polytopes.

Journal Article Type Article
Online Publication Date Oct 10, 2013
Publication Date Jan 1, 2014
Deposit Date Mar 19, 2012
Publicly Available Date Mar 19, 2014
Journal Israel Journal of Mathematics
Print ISSN 0021-2172
Electronic ISSN 1565-8511
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 199
Issue 1
Pages 113-161
DOI https://doi.org/10.1007/s11856-013-0046-3
Public URL https://durham-repository.worktribe.com/output/1502103

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