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It is well known that there is a tiling of $R^{n}$ by crosses for all $n.$ AlBdaiwi and the first author proved that if $2n+1$ is not a prime then there are $2^{\\aleph_{0}}$ \\ non-congruent regular (= face-to-face) tilings of $R^{n}$ by crosses, while there is a unique tiling of $R^{n}$ by crosses for $n=2,3$. They conjectured that this is always the case if $2n+1$ is a prime. To support the conjecture we prove in this paper that also for $R^{5}$ there is a unique regular, and no non-regular"},"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":"1206.4436","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-06-20T10:01:55Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"5afa37b7e3db0d625729d9188f5a661b14af3da1d815877f206341dfa73c4164","abstract_canon_sha256":"e0e914f35d5661538fd94fef4cd85368814f4b0cc39ad83c9a8c46f0f469bcb1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:46.803715Z","signature_b64":"d+GA19BUON/vuZV5Dmv3YQe+5Kom6gs2cxRzWMu2DBq5Mynd0sn+DPtjBRALnEs1NBVqgQKiNc2bZmw+LaVtBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92a62b4b88a1bc9a274f197f8cc9a3a42efaf1f92b3707191b8fa17820b20a6e","last_reissued_at":"2026-05-18T02:42:46.803280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:46.803280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tiling $R^{5}$ by Crosses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Peter Horak, Viliam Hromada","submitted_at":"2012-06-20T10:01:55Z","abstract_excerpt":"An $n$-dimensional cross comprises $2n+1$ unit cubes: the center cube and reflections in all its faces. 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