{"id":"https://openalex.org/W4412864903","doi":"https://doi.org/10.1107/s1600576725005631","title":"Fundamental motifs and parity within the crystallographic point groups","display_name":"Fundamental motifs and parity within the crystallographic point groups","publication_year":2025,"publication_date":"2025-07-10","ids":{"openalex":"https://openalex.org/W4412864903","doi":"https://doi.org/10.1107/s1600576725005631","pmid":"https://pubmed.ncbi.nlm.nih.gov/40765962","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/12321018"},"language":"en","primary_location":{"id":"doi:10.1107/s1600576725005631","doi":"https://doi.org/10.1107/s1600576725005631","is_oa":true,"landing_page_url":"https://doi.org/10.1107/s1600576725005631","pdf_url":"https://journals.iucr.org/j/issues/2025/04/00/dv5024/dv5024.pdf","source":{"id":"https://openalex.org/S79162954","display_name":"Journal of Applied Crystallography","issn_l":"0021-8898","issn":["0021-8898","1600-5767"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Crystallography","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://journals.iucr.org/j/issues/2025/04/00/dv5024/dv5024.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086576148","display_name":"Maureen M. Julian","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Maureen M. Julian","raw_affiliation_strings":["Department of Materials Science and Engineering, Virginia Tech, Blacksburg, VA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Materials Science and Engineering, Virginia Tech, Blacksburg, VA, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"last","author":{"id":null,"display_name":"Matthew Macauley","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matthew Macauley","raw_affiliation_strings":["School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC, USA","institution_ids":["https://openalex.org/I8078737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086576148"],"corresponding_institution_ids":["https://openalex.org/I8078737","https://openalex.org/I859038795"],"apc_list":{"value":5110,"currency":"USD","value_usd":5110},"apc_paid":{"value":5110,"currency":"USD","value_usd":5110},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.29045062,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"58","issue":"4","first_page":"1447","last_page":"1454"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9003999829292297,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9003999829292297,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10939","display_name":"Crystal Structures and Properties","score":0.042500000447034836,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.018699999898672104,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/crystallographic-point-groups","display_name":"crystallographic point groups","score":0.9769999980926514},{"id":"https://openalex.org/keywords/hasse-diagrams","display_name":"Hasse diagrams","score":0.9010000228881836},{"id":"https://openalex.org/keywords/crystal-systems","display_name":"crystal systems","score":0.6119999885559082},{"id":"https://openalex.org/keywords/parity","display_name":"parity","score":0.6819999814033508},{"id":"https://openalex.org/keywords/structural-motifs","display_name":"structural motifs","score":0.7870000004768372},{"id":"https://openalex.org/keywords/conjugacy-classes","display_name":"conjugacy classes","score":0.8370000123977661}],"concepts":[{"id":"https://openalex.org/C57796230","wikidata":"https://www.wikidata.org/wiki/Q899720","display_name":"Point group","level":2,"score":0.7382135391235352},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.6886117458343506},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5321300029754639},{"id":"https://openalex.org/C61276311","wikidata":"https://www.wikidata.org/wiki/Q624543","display_name":"Monoclinic crystal system","level":3,"score":0.5045253038406372},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.4991638660430908},{"id":"https://openalex.org/C140002607","wikidata":"https://www.wikidata.org/wiki/Q901446","display_name":"Hasse diagram","level":3,"score":0.49184322357177734},{"id":"https://openalex.org/C132677234","wikidata":"https://www.wikidata.org/wiki/Q3273544","display_name":"Structural motif","level":2,"score":0.4901631772518158},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4622160792350769},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.4387734532356262},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.21925342082977295},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19866833090782166},{"id":"https://openalex.org/C184779094","wikidata":"https://www.wikidata.org/wiki/Q26383","display_name":"Atomic physics","level":1,"score":0.0581611692905426},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1107/s1600576725005631","doi":"https://doi.org/10.1107/s1600576725005631","is_oa":true,"landing_page_url":"https://doi.org/10.1107/s1600576725005631","pdf_url":"https://journals.iucr.org/j/issues/2025/04/00/dv5024/dv5024.pdf","source":{"id":"https://openalex.org/S79162954","display_name":"Journal of Applied Crystallography","issn_l":"0021-8898","issn":["0021-8898","1600-5767"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Crystallography","raw_type":"journal-article"},{"id":"pmh:oai:pubmedcentral.nih.gov:12321018","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12321018","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"J Appl Crystallogr","raw_type":"Text"},{"id":"pmid:40765962","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40765962","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of applied crystallography","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1107/s1600576725005631","doi":"https://doi.org/10.1107/s1600576725005631","is_oa":true,"landing_page_url":"https://doi.org/10.1107/s1600576725005631","pdf_url":"https://journals.iucr.org/j/issues/2025/04/00/dv5024/dv5024.pdf","source":{"id":"https://openalex.org/S79162954","display_name":"Journal of Applied Crystallography","issn_l":"0021-8898","issn":["0021-8898","1600-5767"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Crystallography","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6631752358","display_name":null,"funder_award_id":"358242","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412864903.pdf","grobid_xml":"https://content.openalex.org/works/W4412864903.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2069624068","https://openalex.org/W2082137322","https://openalex.org/W2084264380","https://openalex.org/W4231244676"],"related_works":["https://openalex.org/W4387064837","https://openalex.org/W2034773824","https://openalex.org/W2038004636","https://openalex.org/W2037925699","https://openalex.org/W116052227","https://openalex.org/W2192872602","https://openalex.org/W2616976730","https://openalex.org/W3124417353","https://openalex.org/W612876017","https://openalex.org/W4237459188"],"abstract_inverted_index":{"This":[0],"paper":[1],"analyzes":[2],"the":[3,10,32,45,66,89,99,109,136,157,168,180,183,194],"Hasse":[4,67,184],"diagram,":[5],"or":[6,69,79,130],"family":[7,70],"tree,":[8],"of":[9,34,44,112,151,156,170,179,193],"3D":[11,113],"crystal":[12,17,27,173],"classes,":[13],"also":[14],"called":[15,93,103],"geometric":[16],"classes.":[18],"The":[19,51,175],"32":[20,110],"point-group":[21],"classes":[22,111],"are":[23,37,92,102,141,189],"partitioned":[24],"into":[25],"seven":[26],"systems.":[28],"In":[29,86,134],"this":[30],"paper,":[31],"structures":[33],"these":[35],"systems":[36],"analyzed,":[38],"leading":[39],"to":[40,58],"a":[41,75,118],"new":[42],"understanding":[43],"relationships":[46],"among":[47],"and":[48,96,98,106],"within":[49],"them.":[50],"point":[52,114,139,160,196],"groups,":[53,115],"including":[54],"their":[55],"subgroups":[56],"up":[57],"conjugacy,":[59],"appear":[60,125,146],"in":[61,65,122,126,143,147],"six":[62],"structural":[63,177],"motifs":[64,91,101,181],"diagram":[68,185],"tree.":[71],"Each":[72],"motif":[73],"has":[74],"parity":[76],"\u2013":[77,81],"even":[78,100,129],"odd":[80,90,132],"that":[82,123,144,187],"determines":[83],"its":[84],"structure.":[85],"three":[87,137],"dimensions,":[88],"monads,":[94],"trigonals":[95],"cubics,":[97],"dyads,":[104],"tetragonals":[105],"hexagonals.":[107],"Of":[108],"29":[116],"have":[117],"well":[119],"defined":[120],"parity,":[121],"they":[124,145,188],"either":[127],"an":[128,131,163,171],"motif.":[133],"contrast,":[135],"monoclinic":[138],"groups":[140,161],"`ambidextrous',":[142],"two":[148],"motifs,":[149],"one":[150],"each":[152],"parity.":[153],"An":[154],"analysis":[155],"ten":[158],"2D":[159],"reveals":[162],"analogous":[164],"structure,":[165],"except":[166],"for":[167],"presence":[169],"ambidextrous":[172],"system.":[174],"striking":[176],"uniformity":[178],"across":[182],"confirms":[186],"essential":[190],"building":[191],"blocks":[192],"crystallographic":[195],"groups.":[197]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2025-10-10T00:00:00"}
