{"paper":{"title":"Orbits of crystallographic embedding of non-crystallographic groups and applications to virology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.MG","math.MP"],"primary_cat":"math-ph","authors_text":"Emilio Zappa, Motiejus Valiunas, Reidun Twarock","submitted_at":"2014-11-08T13:00:58Z","abstract_excerpt":"The architecture of infinite structures with non-crystallographic symmetries can be modeled via aperiodic tilings, but a systematic construction method for finite structures with non-crystallographic symmetry at different radial levels is still lacking. We present here a group theoretical method for the construction of finite nested point set with non-crystallographic symmetry. Akin to the construction of quasicrystals, we embed a non-crystallographic group $G$ into the point group $\\mathcal{P}$ of a higher dimensional lattice and construct the chains of all $G$-containing subgroups. We determ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2115","kind":"arxiv","version":4},"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"}