{"id":"https://openalex.org/W7220650358","doi":"https://doi.org/10.48550/arxiv.2610.03786","title":"Tilings of Closed Surfaces by Congruent Most Curvilinear Polygons","display_name":"Tilings of Closed Surfaces by Congruent Most Curvilinear Polygons","publication_year":2026,"publication_date":"2026-09-30","ids":{"openalex":"https://openalex.org/W7220650358","doi":"https://doi.org/10.48550/arxiv.2610.03786"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03786","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03786","pdf_url":"https://arxiv.org/pdf/2610.03786","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.03786","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157726380","display_name":"Haofang Sun","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sun, Haofang","raw_affiliation_strings":["University of Science and Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Science and Technology","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015336322","display_name":"Min Yan","orcid":"https://orcid.org/0000-0002-7509-4529","observed_orcids":["https://orcid.org/0000-0002-7509-4529"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yan, Min","raw_affiliation_strings":["University of Science and Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Science and Technology","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9390000104904175,"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"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9390000104904175,"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"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.03689999878406525,"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"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.005200000014156103,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/branched-coverings","display_name":"branched coverings","score":0.8899999856948853},{"id":"https://openalex.org/keywords/constant-curvature-metrics","display_name":"constant curvature metrics","score":0.8130000233650208},{"id":"https://openalex.org/keywords/planar-diagrams","display_name":"planar diagrams","score":0.9300000071525574},{"id":"https://openalex.org/keywords/hyperbolic-tilings","display_name":"hyperbolic tilings","score":0.9179999828338623},{"id":"https://openalex.org/keywords/subgroups-of-finite-index","display_name":"finite index subgroups","score":0.7250000238418579}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8300999999046326},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7263000011444092},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5605999827384949},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.45010000467300415},{"id":"https://openalex.org/C98343798","wikidata":"https://www.wikidata.org/wiki/Q1790208","display_name":"Curvilinear coordinates","level":2,"score":0.43369999527931213},{"id":"https://openalex.org/C21550011","wikidata":"https://www.wikidata.org/wiki/Q7632143","display_name":"Substitution tiling","level":2,"score":0.4156999886035919},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.4059000015258789},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.40149998664855957},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.38850000500679016},{"id":"https://openalex.org/C2779668893","wikidata":"https://www.wikidata.org/wiki/Q2250422","display_name":"Constant curvature","level":3,"score":0.37880000472068787},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.3736000061035156},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.37310001254081726},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C35908053","wikidata":"https://www.wikidata.org/wiki/Q3063631","display_name":"Hexagonal tiling","level":3,"score":0.32659998536109924},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.3142000138759613},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C178650486","wikidata":"https://www.wikidata.org/wiki/Q1128619","display_name":"Square tiling","level":3,"score":0.30079999566078186},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3003000020980835},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.2953000068664551},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.2766000032424927},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C43817857","wikidata":"https://www.wikidata.org/wiki/Q9357547","display_name":"Tessellation (computer graphics)","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03786","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03786","pdf_url":"https://arxiv.org/pdf/2610.03786","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.03786","doi":"https://doi.org/10.48550/arxiv.2610.03786","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03786","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.03786","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03786","pdf_url":"https://arxiv.org/pdf/2610.03786","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220650358.pdf","grobid_xml":"https://content.openalex.org/works/W7220650358.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7124148593"],"related_works":["https://openalex.org/W2049554159","https://openalex.org/W7100075555","https://openalex.org/W7098804379","https://openalex.org/W4404913831","https://openalex.org/W2114054207","https://openalex.org/W3093141539","https://openalex.org/W7157676559","https://openalex.org/W2963591214","https://openalex.org/W1998421418","https://openalex.org/W2885390903"],"abstract_inverted_index":{"We":[0,55],"study":[1],"tilings":[2,14,69,91],"of":[3,41,53,75,79,89,116,135],"closed":[4,34],"surfaces":[5],"by":[6,19],"congruent":[7],"most":[8],"curvilinear":[9],"polygons.":[10],"By":[11],"relating":[12],"such":[13],"to":[15,37,68,132],"branched":[16],"coverings":[17,67],"determined":[18],"planar":[20,99],"diagrams":[21],"and":[22,28,51,101],"vertex":[23,94,102],"types,":[24,95],"we":[25],"establish":[26],"necessary":[27],"sufficient":[29],"conditions":[30],"for":[31],"a":[32,39,45],"given":[33],"topological":[35],"surface":[36],"admit":[38],"metric":[40],"constant":[42],"curvature":[43],"supporting":[44],"tiling":[46,119],"with":[47,70,92,128],"prescribed":[48,93],"combinatorial":[49],"data":[50],"number":[52,134],"tiles.":[54,136],"also":[56,112],"characterize":[57],"minimal":[58,90],"tilings,":[59],"which":[60],"do":[61],"not":[62],"descend":[63],"through":[64],"nontrivial":[65],"unbranched":[66],"fewer":[71],"tiles,":[72],"in":[73],"terms":[74],"common":[76],"block":[77],"decompositions":[78],"the":[80,98,107,117,129,133],"associated":[81],"permutations.":[82],"Explicit":[83],"permutation":[84],"constructions":[85],"yield":[86],"infinite":[87],"families":[88],"even":[96],"when":[97],"diagram":[100],"types":[103],"are":[104,123],"fixed.":[105],"In":[106],"hyperbolic":[108],"setting,":[109],"these":[110],"results":[111],"give":[113],"finite-index":[114],"subgroups":[115],"universal":[118],"symmetry":[120],"groups":[121],"that":[122],"maximal":[124],"among":[125],"torsion-free":[126],"subgroups,":[127],"index":[130],"equal":[131]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}
