arXiv:2610.33053v1 Announce Type: new 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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