{"id":"https://openalex.org/W4245728343","doi":"https://doi.org/10.37236/966","title":"Tilings of the sphere with right triangles III: the asymptotically obtuse families","display_name":"Tilings of the sphere with right triangles III: the asymptotically obtuse families","publication_year":2007,"publication_date":"2007-07-05","ids":{"openalex":"https://openalex.org/W4245728343","doi":"https://doi.org/10.37236/966"},"language":"en","primary_location":{"id":"doi:10.37236/966","is_oa":true,"landing_page_url":"https://doi.org/10.37236/966","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r48/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/v14i1r48/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021230588","display_name":"Robert J. MacG. Dawson","orcid":"https://orcid.org/0000-0002-4112-0418"},"institutions":[{"id":"https://openalex.org/I66890659","display_name":"Saint Mary's University","ror":"https://ror.org/010zh7098","country_code":"CA","type":"education","lineage":["https://openalex.org/I66890659"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Robert J. MacG. Dawson","raw_affiliation_strings":["Department of Mathematics and Computing Science Saint Mary's University Halifax, Nova Scotia, Canada","HB Studios Multimedia Ltd. Lunenburg, Nova Scotia, Canada B0J 2C0"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computing Science Saint Mary's University Halifax, Nova Scotia, Canada","institution_ids":["https://openalex.org/I66890659"]},{"raw_affiliation_string":"HB Studios Multimedia Ltd. Lunenburg, Nova Scotia, Canada B0J 2C0","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036890783","display_name":"Blair Doyle","orcid":null},"institutions":[{"id":"https://openalex.org/I66890659","display_name":"Saint Mary's University","ror":"https://ror.org/010zh7098","country_code":"CA","type":"education","lineage":["https://openalex.org/I66890659"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Blair Doyle","raw_affiliation_strings":["HB Studios Multimedia Ltd. Lunenburg, Nova Scotia, Canada B0J 2C0","Department of Mathematics and Computing Science Saint Mary's University Halifax, Nova Scotia, Canada"],"affiliations":[{"raw_affiliation_string":"HB Studios Multimedia Ltd. Lunenburg, Nova Scotia, Canada B0J 2C0","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics and Computing Science Saint Mary's University Halifax, Nova Scotia, Canada","institution_ids":["https://openalex.org/I66890659"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021230588"],"corresponding_institution_ids":["https://openalex.org/I66890659"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.37305913,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"14","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9926000237464905,"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/T10306","display_name":"Liquid Crystal Research Advancements","score":0.9793999791145325,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7959531545639038},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7759258151054382},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.7403159141540527},{"id":"https://openalex.org/keywords/tile","display_name":"Tile","score":0.6872777342796326},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.344191312789917},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09363403916358948},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.043690770864486694},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.04249724745750427}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7959531545639038},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7759258151054382},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.7403159141540527},{"id":"https://openalex.org/C2780728851","wikidata":"https://www.wikidata.org/wiki/Q468402","display_name":"Tile","level":2,"score":0.6872777342796326},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.344191312789917},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09363403916358948},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.043690770864486694},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.04249724745750427},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/966","is_oa":true,"landing_page_url":"https://doi.org/10.37236/966","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r48/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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.101.499","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.101.499","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_14/PDF/v14i1r48.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/966","is_oa":true,"landing_page_url":"https://doi.org/10.37236/966","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r48/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":[{"id":"https://openalex.org/G6358621934","display_name":null,"funder_award_id":"NSERC USRA","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320318328","display_name":"Universities Space Research Association","ror":"https://ror.org/043pgqy52"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4245728343.pdf","grobid_xml":"https://content.openalex.org/works/W4245728343.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1603130817","https://openalex.org/W2085749572","https://openalex.org/W2105335308","https://openalex.org/W2146249205","https://openalex.org/W2578160552","https://openalex.org/W6671608560"],"related_works":["https://openalex.org/W2114959296","https://openalex.org/W38346124","https://openalex.org/W2502442966","https://openalex.org/W2138666621","https://openalex.org/W2383936314","https://openalex.org/W2777914781","https://openalex.org/W1992771654","https://openalex.org/W4246369972","https://openalex.org/W4244869112","https://openalex.org/W2581250438"],"abstract_inverted_index":{"Sommerville":[0],"and":[1,54,68],"Davies":[2],"classified":[3,50],"the":[4,10,18,31],"spherical":[5],"triangles":[6,35,49],"that":[7,56],"can":[8],"tile":[9],"sphere":[11],"in":[12,40],"an":[13],"edge-to-edge":[14,19],"fashion.":[15],"However,":[16],"if":[17],"restriction":[20],"is":[21],"relaxed,":[22],"there":[23],"are":[24],"other":[25],"such":[26],"triangles;":[27],"here,":[28],"we":[29],"continue":[30],"classification":[32],"of":[33,48,65],"right":[34],"with":[36],"this":[37],"property":[38],"begun":[39],"our":[41],"earlier":[42],"papers.":[43],"We":[44],"consider":[45],"six":[46],"families":[47],"as":[51],"\"asymptotically":[52],"obtuse\",":[53],"show":[55],"they":[57],"contain":[58],"two":[59],"non-edge-to-edge":[60],"tiles,":[61],"one":[62],"(with":[63],"angles":[64],"$90^\\circ$,":[66],"$105^\\circ$":[67],"$45^\\circ)$":[69],"believed":[70],"to":[71],"be":[72],"previously":[73],"unknown.":[74]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}