{"paper":{"title":"An algorithmic approach for computing fundamental domains of crystallographic groups","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.CG","math.GR"],"primary_cat":"math.MG","authors_text":"Alice C. Niemeyer, Lukas Schnelle, Reymond Akpanya","submitted_at":"2026-07-02T13:06:56Z","abstract_excerpt":"A crystallographic group is a discrete subgroup of the Euclidean group $\\operatorname{E}(n)$ that has a compact fundamental domain. Since such a crystallographic group $\\Gamma$ is infinite, computing fundamental domains of $\\Gamma$ is algorithmically challenging. We address this difficulty by targeting the computation of Dirichlet cells that can form fundamental domains of $\\Gamma$. We show that the half-spaces defining such a Dirichlet cell can be derived from elements of $\\Gamma$ acting on $\\mathbb{R}^n$ that can be expressed as words of bounded length in a suitable generating set. Based on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02130","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.02130/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}