{"paper":{"title":"Rotation Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Donald Silberger, Sylvia Silberger","submitted_at":"2018-02-25T22:16:30Z","abstract_excerpt":"A query, about the orbit $P{\\cal W}$ in real 3-space of a point $P$ under an isometry group ${\\cal W}$ generated by edge rotations of a tetrahedron, leads to contrasting notions, ${\\cal W}$ versus ${\\cal S}$, of \"rotation group\". The set R $=\\{r_{{\\sf A}_1},r_{{\\sf A}_2}\\}$ of rotations $r_{{\\sf A} _i}$ about axes ${\\sf A}_i$ generates two manifestations of an isometry group on $\\Re^3$:\n  (1). In the {\\em stationary} group ${\\cal S:=S}$(R), all axes {\\sf B} are fixed under a rotation $r_{\\sf A}$ about {\\sf A}.\n  (2). In the {\\em peripatetic} group ${\\cal W:=W}$(R), each $r_{\\sf A}$ transforms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09097","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"}