{"paper":{"title":"Regular prism tilings in $\\SLR$ space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Jen\\H{o} Szirmai","submitted_at":"2012-06-20T08:13:25Z","abstract_excerpt":"$\\SLR$ geometry is one of the eight 3-dimensional Thurston geometries, it can be derived from the 3-dimensional Lie group of all $2\\times 2$ real matrices with determinant one.\n  Our aim is to describe and visualize the {\\it regular infinite (torus-like) or bounded} $p$-gonal prism tilings in $\\SLR$ space. For this purpose we introduce the notion of the infinite and bounded prisms, prove that there exist infinite many regular infinite $p$-gonal face-to-face prism tilings $\\cT^i_p(q)$ and infinitely many regular (bounded) $p$-gonal non-face-to-face $\\SLR$ prism tilings $\\cT_p(q)$ for parameters"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4408","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"}