#### Volume 12, issue 4 (2012)

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

### Alexander Kolpakov

Algebraic & Geometric Topology 12 (2012) 1941–1960
##### 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