https://w3id.org/np/RA9KgA_oAKYi6OFeQf8poArZi3nK6uqiRjn_jBfP2US4k/Head https://w3id.org/np/RA9KgA_oAKYi6OFeQf8poArZi3nK6uqiRjn_jBfP2US4k http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RA9KgA_oAKYi6OFeQf8poArZi3nK6uqiRjn_jBfP2US4k/assertion https://w3id.org/np/RA9KgA_oAKYi6OFeQf8poArZi3nK6uqiRjn_jBfP2US4k http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RA9KgA_oAKYi6OFeQf8poArZi3nK6uqiRjn_jBfP2US4k/provenance https://w3id.org/np/RA9KgA_oAKYi6OFeQf8poArZi3nK6uqiRjn_jBfP2US4k http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RA9KgA_oAKYi6OFeQf8poArZi3nK6uqiRjn_jBfP2US4k/pubinfo https://w3id.org/np/RA9KgA_oAKYi6OFeQf8poArZi3nK6uqiRjn_jBfP2US4k http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RA9KgA_oAKYi6OFeQf8poArZi3nK6uqiRjn_jBfP2US4k/assertion https://w3id.org/delphi/resource/claim/bravais1850-01 http://purl.org/dc/terms/description A regular point assemblage (lattice) can possess only axes of binary, ternary, quaternary or senary symmetry. https://w3id.org/delphi/resource/claim/bravais1850-01 http://purl.org/dc/terms/type theoretical https://w3id.org/delphi/resource/claim/bravais1850-01 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/Claim https://w3id.org/delphi/resource/claim/bravais1850-01 http://www.w3.org/2000/01/rdf-schema#comment Formalization: one. The crystallographic restriction. A Lean target: 2 cos(2 pi/n) in Z implies n in {1,2,3,4,6}. https://w3id.org/delphi/resource/claim/bravais1850-01 http://www.w3.org/2000/01/rdf-schema#comment Related claim <https://w3id.org/delphi/resource/claim/thompson1917-ch09-17> (premise-of): Thompson's argument that the regular dodecahedral and icosahedral radiolarian shells are not crystal-like space partitions takes the crystallographic restriction as its premise: five-fold axes cannot occur in a lattice, so a regular pentagonal dodecahedron in an organism must arise another way. The organism is the contrast case, not a counterexample to the theorem. https://w3id.org/delphi/resource/claim/bravais1850-01 http://www.w3.org/2000/01/rdf-schema#label A lattice can only have two-, three-, four- or six-fold symmetry axes https://w3id.org/delphi/resource/claim/bravais1850-01 http://www.w3.org/2004/02/skos/core#notation n \in \{1,2,3,4,6\} https://w3id.org/delphi/resource/claim/bravais1850-01 http://www.w3.org/2004/02/skos/core#related https://w3id.org/delphi/resource/claim/thompson1917-ch09-17 https://w3id.org/delphi/resource/claim/bravais1850-01 https://w3id.org/delphi/ontology/context Bravais A, “Mémoire sur les systèmes formés par des points distribués régulièrement sur un plan ou dans l'espace”, Journal de l'École Polytechnique 19 (cahier 33), 1850; read in Études cristallographiques, Gauthier-Villars, Paris, 1866 (1850); Mémoire sur les systèmes de points, théorème XLVI, p. 73. Scope: All three-dimensional lattices. https://w3id.org/np/RA9KgA_oAKYi6OFeQf8poArZi3nK6uqiRjn_jBfP2US4k/provenance https://archive.org/details/tudescristallog00bravgoog http://purl.org/dc/terms/bibliographicCitation Bravais A. Mémoire sur les systèmes formés par des points distribués régulièrement sur un plan ou dans l'espace. Journal de l'École Polytechnique 19 (cahier 33), 1850; read in Études cristallographiques, Gauthier-Villars, Paris, 1866 (1850), 1-128 https://archive.org/details/tudescristallog00bravgoog http://purl.org/dc/terms/creator Auguste Bravais https://archive.org/details/tudescristallog00bravgoog http://purl.org/dc/terms/date 1850 https://archive.org/details/tudescristallog00bravgoog http://purl.org/dc/terms/description The posthumous 1866 collection reprints the 1850 memoir on lattices and the 1851 memoir on polyhedra of crystalline form. 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