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On the minimality of the compact right-angled 120-cell

Year: 2026

Type: preprint

Abstract: We prove that a compact right-angled polytope in hyperbolic 4-space has at least 120 facets, with equality only for the right-angled 120-cell. This answers a question of Potyagailo and Vinberg. As a consequence, the right-angled 120-cell is the unique compact right-angled 4-polytope of minimal volume and f-vector.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.33053

Authors: Guo, Lizi, Zheng, Fangting

Institutions: University of Wisconsin–Madison, Xi’an Jiaotong-Liverpool University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

OpenAlex ID: W7223900515

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Cited by: 1

Related to: 10