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

Alexander Kolpakov (1)

1 Département de Mathématiques [Fribourg]

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.

Mots clés: Coxeter polytope; right-angled Coxeter group

Domaines: Géométrie métrique [math.MG]

Alexander Kolpakov. On the optimality of the ideal right-angled 24-cell. Algebraic and Geometric Topology, 2012, 12 (4), pp.1941-1960. ⟨10.2140/agt.2012.12.1941⟩. ⟨hal-00751349v2⟩