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

Kolpakov, Alexander

doi:10.2140/agt.2012.12.1941

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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

Volume 12, issue 4 (2012)