{"paper":{"title":"Hyperball packings in hyperbolic $3$-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Jen\\\"o Szirmai","submitted_at":"2014-05-01T18:43:24Z","abstract_excerpt":"In earlier works \\cite{Sz06-1}, \\cite{Sz06-2}, \\cite{Sz13-3} and \\cite{Sz13-4} we have investigated the densest packings and the least dense coverings by congruent hyperballs (hyperspheres) to the regular prism tilings in $n$-dimensional hyperbolic space $\\HYN$ ($ 3 \\le n \\in \\mathbb{N})$.\n  In this paper we study a large class of hyperball (hypersphere) packings in $3$-dimensional hyperbolic space that can be derived from truncated simplex tilings (e.g. \\cite{S14}, \\cite{MPSz}). It is clear, that in order to get a density upper bound for the above hyperball packings, it is sufficient to deter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0248","kind":"arxiv","version":2},"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"}