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Essential hyperbolic Coxeter polytopes.

Felikson, A. and Tumarkin, P. (2014) 'Essential hyperbolic Coxeter polytopes.', Israel journal of mathematics., 199 (1). pp. 113-161.


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.

Item Type:Article
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Publisher statement:The final publication is available at Springer via
Date accepted:No date available
Date deposited:19 March 2014
Date of first online publication:10 October 2013
Date first made open access:No date available

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