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

  • Lizi Guo
  • Fangting Zheng
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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.

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Cite

BibTeXRIS
BibTeX
@misc{guo2026minimality,
  title = {{On the minimality of the compact right-angled 120-cell}},
  author = {Lizi Guo and Fangting Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33053},
  eprint = {2610.33053},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33053},
}
RIS
TY  - UNPB
TI  - On the minimality of the compact right-angled 120-cell
AU  - Lizi Guo
AU  - Fangting Zheng
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.33053
UR  - https://arxiv.org/abs/2610.33053
AB  - 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.
ER  -