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

TL;DR

This paper proves that the 24-cell is the smallest volume and facet number ideal right-angled hyperbolic polytope in four dimensions, establishing a dimension bound for such polytopes.

Contribution

It establishes the minimal volume and facet count of the 24-cell among four-dimensional ideal right-angled hyperbolic polytopes and derives a dimension bound.

Findings

24-cell has minimal volume among 4D ideal right-angled hyperbolic polytopes

24-cell has minimal facet number among these polytopes

A dimension bound for ideal right-angled hyperbolic polytopes is established

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.