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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1206.4408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-06-20T08:13:25Z","cross_cats_sorted":[],"title_canon_sha256":"8d3c485a8bb4dd56250bc84dd42daa59b2fdbcf612c7a42849f7911743500d9e","abstract_canon_sha256":"b4a693a24094005e6f8d7f2a82f5cf8e80d1599fe2fb58d09901e3cca15d111c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:28.529226Z","signature_b64":"5OMVX176V7MxgYjb52uSoVFu9iYC/BnAO6sY52sf1Csyq9j2AUPYxwj3TcT78MzI6XlCd7cXK64UwGqEVRc+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55e91e93fc97c668e215fe229d35d1e79b0871dec5adef9f3f1a6ef361559809","last_reissued_at":"2026-05-18T01:09:28.528729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:28.528729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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