{"paper":{"title":"Two-sided bounds for the volume of right-angled hyperbolic polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GT","authors_text":"Andrei Vesnin, Du\\v{s}an Repov\\v{s}","submitted_at":"2011-04-18T11:22:05Z","abstract_excerpt":"For a compact right-angled polyhedron $R$ in $\\mathbb H^3$ denote by $\\operatorname{vol} (R)$ the volume and by $\\operatorname{vert} (R)$ the number of vertices. Upper and lower bounds for $\\operatorname{vol} (R)$ in terms of $\\operatorname{vert} (R)$ were obtained in \\cite{A09}. Constructing a 2-parameter family of polyhedra, we show that the asymptotic upper bound $5 v_3 / 8$, where $v_3$ is the volume of the ideal regular tetrahedron in $\\mathbb H^3$, is a double limit point for ratios $\\operatorname{vol} (R) / \\operatorname{vert} (R)$. Moreover, we improve the lower bound in the case $\\ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3437","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}