{"id":"https://openalex.org/W4205326260","doi":"https://doi.org/10.3390/sym14010023","title":"Evidence That Supertriangles Exist in Nature from the Vertical Projections of Koelreuteria paniculata Fruit","display_name":"Evidence That Supertriangles Exist in Nature from the Vertical Projections of Koelreuteria paniculata Fruit","publication_year":2021,"publication_date":"2021-12-24","ids":{"openalex":"https://openalex.org/W4205326260","doi":"https://doi.org/10.3390/sym14010023"},"language":"en","primary_location":{"id":"doi:10.3390/sym14010023","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010023","pdf_url":"https://www.mdpi.com/2073-8994/14/1/23/pdf?version=1640324422","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/1/23/pdf?version=1640324422","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100360827","display_name":"Yuping Li","orcid":"https://orcid.org/0000-0003-4862-4018"},"institutions":[{"id":"https://openalex.org/I167027274","display_name":"Nanjing Forestry University","ror":"https://ror.org/03m96p165","country_code":"CN","type":"education","lineage":["https://openalex.org/I167027274"]},{"id":"https://openalex.org/I4210166603","display_name":"Jinling Institute of Technology","ror":"https://ror.org/05em1gq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210166603"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuping Li","raw_affiliation_strings":["Bamboo Research Institute, Nanjing Forestry University, Nanjing 210037, China","College of Horticulture, Jinling Institute of Technology, Nanjing 210038, China"],"affiliations":[{"raw_affiliation_string":"Bamboo Research Institute, Nanjing Forestry University, Nanjing 210037, China","institution_ids":["https://openalex.org/I167027274"]},{"raw_affiliation_string":"College of Horticulture, Jinling Institute of Technology, Nanjing 210038, China","institution_ids":["https://openalex.org/I4210166603"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007478094","display_name":"Brady K. Quinn","orcid":"https://orcid.org/0000-0001-5781-7087"},"institutions":[{"id":"https://openalex.org/I1319689352","display_name":"Fisheries and Oceans Canada","ror":"https://ror.org/02qa1x782","country_code":"CA","type":"funder","lineage":["https://openalex.org/I1319689352","https://openalex.org/I2802286613"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Brady K. Quinn","raw_affiliation_strings":["Fisheries and Oceans Canada, St. Andrews, NB E5B 0E4, Canada"],"affiliations":[{"raw_affiliation_string":"Fisheries and Oceans Canada, St. Andrews, NB E5B 0E4, Canada","institution_ids":["https://openalex.org/I1319689352"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037636771","display_name":"Johan Gielis","orcid":"https://orcid.org/0000-0002-4536-3839"},"institutions":[{"id":"https://openalex.org/I149213910","display_name":"University of Antwerp","ror":"https://ror.org/008x57b05","country_code":"BE","type":"education","lineage":["https://openalex.org/I149213910"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Johan Gielis","raw_affiliation_strings":["Department of Biosciences Engineering, University of Antwerp, B-2020 Antwerp, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Biosciences Engineering, University of Antwerp, B-2020 Antwerp, Belgium","institution_ids":["https://openalex.org/I149213910"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100677898","display_name":"Yirong Li","orcid":"https://orcid.org/0000-0003-4497-0001"},"institutions":[{"id":"https://openalex.org/I4210166603","display_name":"Jinling Institute of Technology","ror":"https://ror.org/05em1gq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210166603"]},{"id":"https://openalex.org/I167027274","display_name":"Nanjing Forestry University","ror":"https://ror.org/03m96p165","country_code":"CN","type":"education","lineage":["https://openalex.org/I167027274"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yirong Li","raw_affiliation_strings":["Bamboo Research Institute, Nanjing Forestry University, Nanjing 210037, China","College of Horticulture, Jinling Institute of Technology, Nanjing 210038, China"],"affiliations":[{"raw_affiliation_string":"Bamboo Research Institute, Nanjing Forestry University, Nanjing 210037, China","institution_ids":["https://openalex.org/I167027274"]},{"raw_affiliation_string":"College of Horticulture, Jinling Institute of Technology, Nanjing 210038, China","institution_ids":["https://openalex.org/I4210166603"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091449787","display_name":"Peijian Shi","orcid":"https://orcid.org/0000-0003-4696-0130"},"institutions":[{"id":"https://openalex.org/I167027274","display_name":"Nanjing Forestry University","ror":"https://ror.org/03m96p165","country_code":"CN","type":"education","lineage":["https://openalex.org/I167027274"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Peijian Shi","raw_affiliation_strings":["Bamboo Research Institute, Nanjing Forestry University, Nanjing 210037, China"],"affiliations":[{"raw_affiliation_string":"Bamboo Research Institute, Nanjing Forestry University, Nanjing 210037, China","institution_ids":["https://openalex.org/I167027274"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5091449787"],"corresponding_institution_ids":["https://openalex.org/I167027274"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.9924,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.87435507,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"14","issue":"1","first_page":"23","last_page":"23"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14365","display_name":"Leaf Properties and Growth Measurement","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T14365","display_name":"Leaf Properties and Growth Measurement","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9860000014305115,"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/T12729","display_name":"Tree Root and Stability Studies","score":0.9711999893188477,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5858385562896729},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4942474663257599},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4727255702018738},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.449459433555603},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.44217023253440857},{"id":"https://openalex.org/keywords/symmetry-in-biology","display_name":"Symmetry in biology","score":0.4261389970779419},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.34844332933425903},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30315470695495605},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16797024011611938}],"concepts":[{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5858385562896729},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4942474663257599},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4727255702018738},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.449459433555603},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.44217023253440857},{"id":"https://openalex.org/C64089718","wikidata":"https://www.wikidata.org/wiki/Q598159","display_name":"Symmetry in biology","level":2,"score":0.4261389970779419},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.34844332933425903},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30315470695495605},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16797024011611938},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym14010023","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010023","pdf_url":"https://www.mdpi.com/2073-8994/14/1/23/pdf?version=1640324422","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:c:irua:186453","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401849","display_name":"Institutional Repository University of Antwerp (University of Antwerp)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149213910","host_organization_name":"University of Antwerp","host_organization_lineage":["https://openalex.org/I149213910"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:doaj.org/article:a981d23cfdf947e49a02cc7308aa207a","is_oa":true,"landing_page_url":"https://doaj.org/article/a981d23cfdf947e49a02cc7308aa207a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 1, p 23 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/1/23/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14010023","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14010023","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010023","pdf_url":"https://www.mdpi.com/2073-8994/14/1/23/pdf?version=1640324422","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8899999856948853,"id":"https://metadata.un.org/sdg/14","display_name":"Life below water"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4205326260.pdf","grobid_xml":"https://content.openalex.org/works/W4205326260.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1964292167","https://openalex.org/W1964903133","https://openalex.org/W2002783521","https://openalex.org/W2035352647","https://openalex.org/W2038868830","https://openalex.org/W2081882777","https://openalex.org/W2088763902","https://openalex.org/W2141270723","https://openalex.org/W2147107252","https://openalex.org/W2165168736","https://openalex.org/W2171074980","https://openalex.org/W2181270626","https://openalex.org/W2518404248","https://openalex.org/W2808729342","https://openalex.org/W2884010546","https://openalex.org/W2900771368","https://openalex.org/W2945550691","https://openalex.org/W3007986735","https://openalex.org/W3016411403","https://openalex.org/W3112540142","https://openalex.org/W3121308055","https://openalex.org/W3177266906","https://openalex.org/W4242044878","https://openalex.org/W4243622662","https://openalex.org/W4246237884","https://openalex.org/W4250807311","https://openalex.org/W6763032661","https://openalex.org/W6766644976"],"related_works":["https://openalex.org/W4398681136","https://openalex.org/W2370332886","https://openalex.org/W3042074040","https://openalex.org/W2414337799","https://openalex.org/W2164293324","https://openalex.org/W2747700891","https://openalex.org/W2064749787","https://openalex.org/W3043363583","https://openalex.org/W2969754558","https://openalex.org/W1991296712"],"abstract_inverted_index":{"Many":[0],"natural":[1,37,157],"radial":[2],"symmetrical":[3,134,178],"shapes":[4,38,135,179],"(e.g.,":[5],"sea":[6],"stars)":[7],"follow":[8],"the":[9,46,68,80,92,110,117,123,130,137,140,144,161,164,184,197],"Gielis":[10],"equation":[11,16],"(GE)":[12],"or":[13,44,48],"its":[14],"twin":[15],"(TGE).":[17],"A":[18],"supertriangle":[19],"(three":[20],"triangles":[21],"arranged":[22],"around":[23],"a":[24,29,64,113],"central":[25],"polygon)":[26],"represents":[27],"such":[28],"shape,":[30,66],"but":[31],"no":[32],"study":[33],"has":[34],"tested":[35],"whether":[36,45],"can":[39,50,180],"be":[40,181],"represented":[41],"as/are":[42],"supertriangles":[43,158],"GE":[47,81,111,138,165],"TGE":[49,131,167],"describe":[51],"their":[52,72,170],"shape.":[53],"We":[54],"collected":[55],"100":[56],"pieces":[57],"of":[58,91,125,146,163,191],"Koelreuteria":[59],"paniculata":[60],"fruit,":[61],"which":[62],"have":[63],"supertriangular":[65],"extracted":[67],"boundary":[69],"coordinates":[70],"for":[71],"vertical":[73],"projections,":[74,109],"and":[75,82,100,166,172],"then":[76],"fitted":[77],"them":[78],"with":[79],"TGE.":[83],"The":[84],"adjusted":[85],"root":[86],"mean":[87],"square":[88],"errors":[89],"(RMSEadj)":[90],"two":[93,141],"equations":[94],"were":[95,102,127],"always":[96],"less":[97,103],"than":[98,104,116,136],"0.08,":[99],">70%":[101],"0.05.":[105],"For":[106],"57/100":[107],"fruit":[108],"had":[112],"lower":[114],"RMSEadj":[115],"TGE,":[118],"although":[119],"overall":[120],"differences":[121],"in":[122,148],"goodness":[124],"fit":[126],"non-significant.":[128],"However,":[129],"produces":[132],"more":[133],"as":[139],"parameters":[142],"controlling":[143],"extent":[145],"symmetry":[147,193],"it":[149],"are":[150],"approximately":[151],"equal.":[152],"This":[153],"work":[154],"demonstrates":[155],"that":[156,174,188],"exist,":[159],"validates":[160],"use":[162],"to":[168],"model":[169],"shapes,":[171],"suggests":[173],"different":[175,189],"complex":[176],"radially":[177],"generated":[182],"by":[183],"same":[185,198],"equation,":[186],"implying":[187],"types":[190],"biological":[192],"may":[194],"result":[195],"from":[196],"biophysical":[199],"mechanisms.":[200]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":5}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}