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On the optimality of the ideal right-angled $24$–cell

Alexander Kolpakov
Algebraic & Geometric Topology 12 (2012) 1941–1960
DOI: 10.2140/agt.2012.12.1941
Abstract

We prove that among four-dimensional ideal right-angled hyperbolic polytopes the 24–cell is of minimal volume and of minimal facet number. As a corollary, a dimension bound for ideal right-angled hyperbolic polytopes is obtained.

Keywords
Coxeter polytope, right-angled Coxeter group
Mathematical Subject Classification 2000
Primary: 20F55
Secondary: 52B11, 51M20
References
Publication
Received: 22 June 2012
Revised: 11 July 2012
Accepted: 17 July 2012
Published: 27 October 2012
Authors
Alexander Kolpakov
Department of Mathematics
University of Fribourg
Chemin du Musée 23
CH-1700 Fribourg
Switzerland