{"id":"https://openalex.org/W2162952575","doi":"https://doi.org/10.1107/s010876730201259x","title":"On the symmetry of simple 12- and 13-hedra","display_name":"On the symmetry of simple 12- and 13-hedra","publication_year":2002,"publication_date":"2002-08-23","ids":{"openalex":"https://openalex.org/W2162952575","doi":"https://doi.org/10.1107/s010876730201259x","mag":"2162952575","pmid":"https://pubmed.ncbi.nlm.nih.gov/12192124"},"language":"en","primary_location":{"id":"doi:10.1107/s010876730201259x","doi":"https://doi.org/10.1107/s010876730201259x","is_oa":false,"landing_page_url":"https://doi.org/10.1107/s010876730201259x","pdf_url":null,"source":{"id":"https://openalex.org/S150871906","display_name":"Acta Crystallographica Section A Foundations of Crystallography","issn_l":"0108-7673","issn":["0108-7673","1600-5724"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Crystallographica Section A Foundations of Crystallography","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012737530","display_name":"Yury L. Voytekhovsky","orcid":"https://orcid.org/0000-0002-5380-9191","observed_orcids":["https://orcid.org/0000-0002-5380-9191"]},"institutions":[{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035"]},{"id":"https://openalex.org/I197524780","display_name":"Petrozavodsk State University","ror":"https://ror.org/0176aa147","country_code":"RU","type":"education","lineage":["https://openalex.org/I197524780"]},{"id":"https://openalex.org/I4210163243","display_name":"Kola Science Centre","ror":"https://ror.org/056wf8856","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210160366","https://openalex.org/I4210163243","https://openalex.org/I4210163714"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Yury L. Voytekhovsky","raw_affiliation_strings":["Laboratory for Mathematical Investigations in Crystallography, Mineralogy and Petrography, High Technologies Centre, Kola Branch of Petrozavodsk State University, 14 Fersman Street, 184209 Apatity, Russia. voyt@geoksc.apatity.ru","Laboratory for Mathematical Investigations in Crystallography, Mineralogy and Petrography, High Technologies Centre, Kola Branch of Petrozavodsk State University, 14 Fersman Street, 184209 Apatity, Russia","Laboratory for Platinum Group Elements Ore Genesis, Geological Institute of the Kola Science Centre, Russian Academy of Sciences, 14 Fersman Street, 184209 Apatity, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Mathematical Investigations in Crystallography, Mineralogy and Petrography, High Technologies Centre, Kola Branch of Petrozavodsk State University, 14 Fersman Street, 184209 Apatity, Russia. voyt@geoksc.apatity.ru","institution_ids":["https://openalex.org/I197524780"]},{"raw_affiliation_string":"Laboratory for Mathematical Investigations in Crystallography, Mineralogy and Petrography, High Technologies Centre, Kola Branch of Petrozavodsk State University, 14 Fersman Street, 184209 Apatity, Russia","institution_ids":["https://openalex.org/I197524780"]},{"raw_affiliation_string":"Laboratory for Platinum Group Elements Ore Genesis, Geological Institute of the Kola Science Centre, Russian Academy of Sciences, 14 Fersman Street, 184209 Apatity, Russia","institution_ids":["https://openalex.org/I1313323035","https://openalex.org/I4210163243"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015806457","display_name":"Dmitry G. Stepenshchikov","orcid":"https://orcid.org/0000-0003-0956-4622","observed_orcids":["https://orcid.org/0000-0003-0956-4622"]},"institutions":[{"id":"https://openalex.org/I197524780","display_name":"Petrozavodsk State University","ror":"https://ror.org/0176aa147","country_code":"RU","type":"education","lineage":["https://openalex.org/I197524780"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Dmitry G. Stepenshchikov","raw_affiliation_strings":["Laboratory for Mathematical Investigations in Crystallography, Mineralogy and Petrography, High Technologies Centre, Kola Branch of Petrozavodsk State University, 14 Fersman Street, 184209 Apatity, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Mathematical Investigations in Crystallography, Mineralogy and Petrography, High Technologies Centre, Kola Branch of Petrozavodsk State University, 14 Fersman Street, 184209 Apatity, Russia","institution_ids":["https://openalex.org/I197524780"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.728,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.77521264,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":93},"biblio":{"volume":"58","issue":"5","first_page":"502","last_page":"505"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.6923999786376953,"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":0.6923999786376953,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.2531999945640564,"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/T12504","display_name":"Mathematics and Applications","score":0.014000000432133675,"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/automorphism-groups","display_name":"automorphism groups","score":0.7720000147819519},{"id":"https://openalex.org/keywords/polyhedral-symmetry","display_name":"polyhedral symmetry","score":0.7730000019073486}],"concepts":[{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.8292129039764404},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.7126303911209106},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6957211494445801},{"id":"https://openalex.org/C57796230","wikidata":"https://www.wikidata.org/wiki/Q899720","display_name":"Point group","level":2,"score":0.6432669162750244},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5859905481338501},{"id":"https://openalex.org/C43122875","wikidata":"https://www.wikidata.org/wiki/Q5428522","display_name":"Facet (psychology)","level":4,"score":0.5590723752975464},{"id":"https://openalex.org/C5534955","wikidata":"https://www.wikidata.org/wiki/Q7661343","display_name":"Symmetry operation","level":3,"score":0.5125164985656738},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4678925573825836},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.42935600876808167},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.41678667068481445},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3752802312374115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34893131256103516},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.3184148073196411},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.2651830315589905},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25537484884262085},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18239793181419373},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C2865642","wikidata":"https://www.wikidata.org/wiki/Q378132","display_name":"Big Five personality traits","level":3,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C187288502","wikidata":"https://www.wikidata.org/wiki/Q641118","display_name":"Personality","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1107/s010876730201259x","doi":"https://doi.org/10.1107/s010876730201259x","is_oa":false,"landing_page_url":"https://doi.org/10.1107/s010876730201259x","pdf_url":null,"source":{"id":"https://openalex.org/S150871906","display_name":"Acta Crystallographica Section A Foundations of Crystallography","issn_l":"0108-7673","issn":["0108-7673","1600-5724"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Crystallographica Section A Foundations of Crystallography","raw_type":"journal-article"},{"id":"pmid:12192124","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/12192124","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":"Acta crystallographica. Section A, Foundations of crystallography","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W2023941716","https://openalex.org/W2025629108","https://openalex.org/W2061051771"],"related_works":["https://openalex.org/W2162387169","https://openalex.org/W2031572572","https://openalex.org/W2917846148","https://openalex.org/W2025629108","https://openalex.org/W1995862733","https://openalex.org/W2061051771","https://openalex.org/W2759994534","https://openalex.org/W2038004636","https://openalex.org/W2192872602","https://openalex.org/W186155015"],"abstract_inverted_index":{"The":[0,25],"symmetry":[1,49],"point":[2,50],"groups":[3],"for":[4,21],"all":[5],"combinatorially":[6],"non-isomorphic":[7],"simple":[8],"12-":[9],"and":[10,13,42,48],"13-hedra":[11],"(7595":[12],"49566,":[14],"respectively)":[15],"are":[16,37],"contributed":[17],"in":[18],"the":[19,22,45],"paper":[20],"first":[23],"time.":[24],"most":[26],"symmetrical":[27],"polyhedra":[28],"with":[29],"automorphism":[30],"group":[31],"orders":[32],"not":[33],"less":[34],"than":[35],"3":[36],"drawn":[38],"as":[39],"Schlegel":[40],"diagrams":[41],"characterized":[43],"by":[44],"facet":[46],"symbols":[47],"groups.":[51]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-09-21T07:43:02.447757","created_date":"2016-06-24T00:00:00"}
