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We prove that this structure can be described by a generalized Calabi construction, that is, E^n/G is represented as the quotient of the Cartesian product of two flat orbifolds under the diagonal action of a structure group of isometries. We determine the structure group and prove that it is finite if and only if the fibered orbifold structure has an orthogonally dual fibered orbifold structure.\n  A geometric fibration of E^n/G cor"},"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":"1112.3981","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-12-16T21:49:24Z","cross_cats_sorted":[],"title_canon_sha256":"b2225800deeec76c49dd01c4b1c6e38cb60fee04543f7e5d446cb7a37e653a2b","abstract_canon_sha256":"4332d257baa8c4e7888e72d3d06a75a51fc9a082e0f8acce4de8c3307dfec417"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:13.605349Z","signature_b64":"WmsKlE3BxaAotXnFFzVgvTp2u8l9FStDs0qAxNUA6Psb+iWfwtbSHHfWeGby1s8TGqrW/7hN7zqMddwn/T/KCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ec1da296eae5bf50527215b62102d7b6a4c34a586aa4892197178666a7cb187","last_reissued_at":"2026-05-18T03:44:13.604962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:13.604962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fibered orbifolds and crystallographic groups, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"John G. 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