{"paper":{"title":"Subgroups of SO(3) Associated with Tilings","license":"","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GR","authors_text":"Charles Radin, Lorenzo Sadun","submitted_at":"1996-01-12T00:00:00Z","abstract_excerpt":"We give a thorough analysis of those subgroups of SO(3) generated by rotations about perpendicular axes by 2\\pi/p and 2\\pi/q. A corollary is that such a group is the free product of the cyclic groups of rotations about the separate axes if and only if p,q\\ge 3 and are both odd. These groups are naturally associated with a family of hierarchical tilings of Euclidean 3-space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9601202","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"}