{"id":"https://openalex.org/W1539293498","doi":"https://doi.org/10.37236/2512","title":"Minimal Covers of the Archimedean Tilings, Part 1","display_name":"Minimal Covers of the Archimedean Tilings, Part 1","publication_year":2012,"publication_date":"2012-07-12","ids":{"openalex":"https://openalex.org/W1539293498","doi":"https://doi.org/10.37236/2512","mag":"1539293498"},"language":"en","primary_location":{"id":"doi:10.37236/2512","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2512","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i3p6/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i3p6/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110349382","display_name":"Daniel Pellicer","orcid":null},"institutions":[{"id":"https://openalex.org/I22675022","display_name":"Williams College","ror":"https://ror.org/04avkmd49","country_code":"US","type":"education","lineage":["https://openalex.org/I22675022"]},{"id":"https://openalex.org/I4210157032","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05e9bn444","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210157032"]}],"countries":["ES","US"],"is_corresponding":true,"raw_author_name":"Daniel Pellicer","raw_affiliation_strings":["Instituto De Matematicas, Unidad Moreli","Williams College"],"affiliations":[{"raw_affiliation_string":"Instituto De Matematicas, Unidad Moreli","institution_ids":["https://openalex.org/I4210157032"]},{"raw_affiliation_string":"Williams College","institution_ids":["https://openalex.org/I22675022"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020896667","display_name":"Gordon Williams","orcid":"https://orcid.org/0000-0002-4980-5921"},"institutions":[{"id":"https://openalex.org/I141472210","display_name":"University of Alaska Fairbanks","ror":"https://ror.org/01j7nq853","country_code":"US","type":"education","lineage":["https://openalex.org/I141472210"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gordon Williams","raw_affiliation_strings":["University of Alaska Fairbanks","National University of Mexico"],"affiliations":[{"raw_affiliation_string":"University of Alaska Fairbanks","institution_ids":["https://openalex.org/I141472210"]},{"raw_affiliation_string":"National University of Mexico","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110349382"],"corresponding_institution_ids":["https://openalex.org/I22675022","https://openalex.org/I4210157032"],"apc_list":null,"apc_paid":null,"fwci":0.6022,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.63907682,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"19","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8163357973098755},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.779266357421875},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7356048822402954},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.7289506793022156},{"id":"https://openalex.org/keywords/flag","display_name":"Flag (linear algebra)","score":0.6924616694450378},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.6892841458320618},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.544276773929596},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.47522619366645813},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.45154309272766113},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.446607381105423},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35045287013053894},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23732036352157593},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.2246834635734558}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8163357973098755},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.779266357421875},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7356048822402954},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.7289506793022156},{"id":"https://openalex.org/C2776730729","wikidata":"https://www.wikidata.org/wiki/Q1392130","display_name":"Flag (linear algebra)","level":3,"score":0.6924616694450378},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.6892841458320618},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.544276773929596},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.47522619366645813},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.45154309272766113},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.446607381105423},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35045287013053894},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23732036352157593},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2246834635734558},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/2512","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2512","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i3p6/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/2512","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2512","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i3p6/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1539293498.pdf","grobid_xml":"https://content.openalex.org/works/W1539293498.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W51037165","https://openalex.org/W266013613","https://openalex.org/W1869822106","https://openalex.org/W1969567487","https://openalex.org/W1977183350","https://openalex.org/W1987949906","https://openalex.org/W2014909874","https://openalex.org/W2017022863","https://openalex.org/W2030343350","https://openalex.org/W2058365359","https://openalex.org/W2065872561","https://openalex.org/W2080182303","https://openalex.org/W2120257244","https://openalex.org/W2324011160"],"related_works":["https://openalex.org/W2963257052","https://openalex.org/W4302155387","https://openalex.org/W2949256963","https://openalex.org/W2545189445","https://openalex.org/W2115024785","https://openalex.org/W2949890955","https://openalex.org/W2085781584","https://openalex.org/W4289596368","https://openalex.org/W1543499813","https://openalex.org/W1678473343"],"abstract_inverted_index":{"We":[0,11],"discuss":[1,48],"representations":[2],"of":[3,8,21,29,36,40,53,66],"non-finite":[4,22],"polyhedra":[5,23],"as":[6],"quotients":[7],"regular":[9,19,51,62],"polytopes.":[10],"provide":[12],"some":[13],"structural":[14],"results":[15],"about":[16,25],"the":[17,26,33,37,41,49,54],"minimal":[18,50,61],"covers":[20,52,63],"and":[24,57],"stabilizer":[27],"subgroups":[28],"their":[30],"flags":[31],"under":[32],"flag":[34],"action":[35],"automorphism":[38],"group":[39],"covering":[42],"polytope.":[43],"As":[44],"motivating":[45],"examples":[46],"we":[47,58],"Archimedean":[55],"tilings,":[56],"construct":[59],"explicit":[60],"for":[64],"three":[65],"them.":[67]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2016-06-24T00:00:00"}