{"paper":{"title":"Fundamental domains for rhombic lattices with dihedral symmetry of order 8","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Dirk Frettl\\\"oh, Joseph Ray Clarence G. Damasco, Manuel Joseph C. Loquias","submitted_at":"2018-04-18T07:16:43Z","abstract_excerpt":"We show by construction that every rhombic lattice $\\Gamma$ in $\\mathbb{R}^{2}$ has a fundamental domain whose symmetry group contains the point group of $\\Gamma$ as a subgroup of index $2$. This solves the last open case of a question raised in [3] on fundamental domains for planar lattices whose symmetry groups properly contain the point groups of the lattices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06577","kind":"arxiv","version":3},"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"}