{"paper":{"title":"Classification of Sol lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Emil Moln\\'ar, Jen\\\"o Szirmai","submitted_at":"2011-06-23T08:07:59Z","abstract_excerpt":"$\\SOL$ geometry is one of the eight homogeneous Thurston 3-geomet-ri-es $$\\EUC, \\SPH, \\HYP, \\SXR, \\HXR, \\SLR, \\NIL, \\SOL.$$ In \\cite{Sz10} the {\\it densest lattice-like translation ball packings} to a type (type {\\bf I/1} in this paper) of $\\SOL$ lattices has been determined. Some basic concept of $\\SOL$ were defined by {\\sc{P. Scott}} in \\cite{S}, in general.\n  In our present work we shall classify $\\SOL$ lattices in an algorithmic way into 17 (seventeen) types, in analogy of the 14 Bravais types of the Euclidean 3-lattices, but infinitely many $\\SOL$ affine equivalence classes, in each type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4646","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"}