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Clearly, any facial angle and any dihedral angle is a multiple of $\\pi/2$.\n  In this note we explore the converse: if the facial and/or dihedral angles are all multiples of $\\pi /2$, is the polyhedron necessarily orthogonal? The case of facial angles was answered previously. In this note we show that if both the facial and dihedral angles are multiples of $\\pi /2$ then the polyhedron is orthogon"},"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":"1312.6824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-24T14:30:00Z","cross_cats_sorted":[],"title_canon_sha256":"5bef1a67adb7ff8a6143e23b015ff62e250a4795174215e195611d418be24ffd","abstract_canon_sha256":"c93cee6158337a03093749f420b480e7ea631ff766f8c5f3b501a594aff17905"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:55.951446Z","signature_b64":"HKqULuakd2+MxQvF9opOzVd7hlsN5qwXXg59u7H3nmFak61d4hdJnKebZw4hogLqn8CwdoMtl8RbE8FStdZ6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4e67d93475b2437feb2384f95cb1956efab9dc4090817b35b87dd675f205c7c","last_reissued_at":"2026-05-18T03:03:55.950706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:55.950706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dihedral angles and orthogonal polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Anna Lubiw, Hamide Vosoughpour, Martin Derka, Stephen Kiazyk, Therese Biedl","submitted_at":"2013-12-24T14:30:00Z","abstract_excerpt":"Consider an orthogonal polyhedron, i.e., a polyhedron where (at least after a suitable rotation) all faces are perpendicular to a coordinate axis, and hence all edges are parallel to a coordinate axis. 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