{"id":"https://openalex.org/W2961958345","doi":"https://doi.org/10.1145/3326229.3326264","title":"On the Number of Congruent Classes of the Tetrahedra Determined by Given Volume, Circumradius and Face Areas","display_name":"On the Number of Congruent Classes of the Tetrahedra Determined by Given Volume, Circumradius and Face Areas","publication_year":2019,"publication_date":"2019-07-08","ids":{"openalex":"https://openalex.org/W2961958345","doi":"https://doi.org/10.1145/3326229.3326264","mag":"2961958345"},"language":"en","primary_location":{"id":"doi:10.1145/3326229.3326264","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3326229.3326264","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"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/A5058328411","display_name":"Zhenbing Zeng","orcid":"https://orcid.org/0000-0002-9728-1114"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhenbing Zeng","raw_affiliation_strings":["Shanghai University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100454252","display_name":"Lu Yang","orcid":"https://orcid.org/0000-0002-1282-9735"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lu Yang","raw_affiliation_strings":["Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu, China"],"affiliations":[{"raw_affiliation_string":"Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu, China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083783779","display_name":"Lydia Dehbi","orcid":"https://orcid.org/0009-0008-6894-7109"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lydia Dehbi","raw_affiliation_strings":["Shanghai University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058328411"],"corresponding_institution_ids":["https://openalex.org/I113940042"],"apc_list":null,"apc_paid":null,"fwci":0.322,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.52953839,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":null,"issue":null,"first_page":"363","last_page":"370"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9915000200271606,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.8841118812561035},{"id":"https://openalex.org/keywords/face","display_name":"Face (sociological concept)","score":0.6814721822738647},{"id":"https://openalex.org/keywords/volume","display_name":"Volume (thermodynamics)","score":0.6155973076820374},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4315977692604065},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40804848074913025},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21572595834732056},{"id":"https://openalex.org/keywords/sociology","display_name":"Sociology","score":0.11599090695381165},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08719295263290405}],"concepts":[{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.8841118812561035},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.6814721822738647},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.6155973076820374},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4315977692604065},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40804848074913025},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21572595834732056},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.11599090695381165},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08719295263290405},{"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/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3326229.3326264","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3326229.3326264","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1767264632","https://openalex.org/W1971022195","https://openalex.org/W1980082798","https://openalex.org/W2104950168","https://openalex.org/W2128967868","https://openalex.org/W2307111655","https://openalex.org/W2350895165","https://openalex.org/W6705465248"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W3118783749","https://openalex.org/W2002583644","https://openalex.org/W3119989344","https://openalex.org/W2025402442","https://openalex.org/W2098990162","https://openalex.org/W1987870972","https://openalex.org/W2993813190","https://openalex.org/W2567351266","https://openalex.org/W1998766989"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"proved":[4],"that":[5,22],"for":[6],"any":[7],"tetrahedron":[8],"T":[9],",":[10],"there":[11],"exists":[12],"at":[13,16],"least":[14],"one,":[15],"most":[17],"eight":[18],"non-congruent":[19],"tetrahedra":[20,38],"so":[21],"they":[23],"share":[24],"the":[25,41,46,61],"same":[26],"volume,":[27],"circumradius":[28],"and":[29,44],"four":[30],"face":[31],"areas.":[32],"We":[33,54],"used":[34],"metric":[35],"invariants":[36],"of":[37,48,63],"to":[39],"construct":[40],"equation":[42],"system":[43],"investigated":[45],"number":[47],"its":[49],"real":[50],"rootswith":[51],"symbolic":[52],"computation.":[53,66],"also":[55],"posed":[56],"one":[57],"open":[58],"problem":[59],"on":[60],"basis":[62],"extensive":[64],"numerical":[65]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}