{"id":"https://openalex.org/W2020111166","doi":"https://doi.org/10.1145/2582112.2582142","title":"Weight Balancing on Boundaries and Skeletons","display_name":"Weight Balancing on Boundaries and Skeletons","publication_year":2014,"publication_date":"2014-05-02","ids":{"openalex":"https://openalex.org/W2020111166","doi":"https://doi.org/10.1145/2582112.2582142","mag":"2020111166"},"language":"en","primary_location":{"id":"doi:10.1145/2582112.2582142","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2582112.2582142","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirtieth annual symposium on Computational geometry","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/A5038157909","display_name":"Luis Barba","orcid":"https://orcid.org/0000-0001-8732-6799"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Luis Barba","raw_affiliation_strings":["Boursier FRIA du FNRS, ULB, Brussels, Belgium, and School of Computer Science, Carleton University, Ottawa, Canada"],"affiliations":[{"raw_affiliation_string":"Boursier FRIA du FNRS, ULB, Brussels, Belgium, and School of Computer Science, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091366247","display_name":"Otfried Cheong","orcid":"https://orcid.org/0000-0003-4467-7075"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Otfried Cheong","raw_affiliation_strings":["Department of Computer Science, KAIST, Daejeon, Korea"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, KAIST, Daejeon, Korea","institution_ids":["https://openalex.org/I157485424"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042440491","display_name":"Jean-Lou De Carufel","orcid":"https://orcid.org/0000-0002-6734-8234"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jean-Lou De Carufel","raw_affiliation_strings":["School of Computer Science, Carleton University, Ottawa, Canada"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071947173","display_name":"Michael Gene Dobbins","orcid":"https://orcid.org/0000-0003-1428-406X"},"institutions":[{"id":"https://openalex.org/I123900574","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12","country_code":"KR","type":"education","lineage":["https://openalex.org/I123900574"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Michael Gene Dobbins","raw_affiliation_strings":["GAIA, POSTECH, Pohang, Korea","GAIA, POSTECH, Pohang, Korea#TAB#"],"affiliations":[{"raw_affiliation_string":"GAIA, POSTECH, Pohang, Korea","institution_ids":["https://openalex.org/I123900574"]},{"raw_affiliation_string":"GAIA, POSTECH, Pohang, Korea#TAB#","institution_ids":["https://openalex.org/I123900574"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112284215","display_name":"Rudolf Fleischer","orcid":null},"institutions":[{"id":"https://openalex.org/I39706905","display_name":"German University of Technology","ror":"https://ror.org/055hq4920","country_code":"OM","type":"education","lineage":["https://openalex.org/I39706905"]},{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN","OM"],"is_corresponding":false,"raw_author_name":"Rudolf Fleischer","raw_affiliation_strings":["IIPL and SCS, Fudan University, Shanghai, P. R. China, and CS, GUtech, Muscat, Oman","IIPL and SCS, Fudan University, Shanghai, P. R. China, and CS, GUtech, Muscat, Oman#TAB#"],"affiliations":[{"raw_affiliation_string":"IIPL and SCS, Fudan University, Shanghai, P. R. China, and CS, GUtech, Muscat, Oman","institution_ids":["https://openalex.org/I39706905","https://openalex.org/I24943067"]},{"raw_affiliation_string":"IIPL and SCS, Fudan University, Shanghai, P. R. China, and CS, GUtech, Muscat, Oman#TAB#","institution_ids":["https://openalex.org/I39706905","https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074573236","display_name":"Akitoshi Kawamura","orcid":"https://orcid.org/0009-0006-3706-7470"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Akitoshi Kawamura","raw_affiliation_strings":["Department of Computer Science, University of Tokyo, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Tokyo, Tokyo, Japan","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012765386","display_name":"Matias Korman","orcid":"https://orcid.org/0000-0002-4880-1101"},"institutions":[{"id":"https://openalex.org/I184597095","display_name":"National Institute of Informatics","ror":"https://ror.org/04ksd4g47","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I184597095","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Matias Korman","raw_affiliation_strings":["National Institute of Informatics, Tokyo, Japan, and JST ERATO, Kawarabayashi Project, Japan"],"affiliations":[{"raw_affiliation_string":"National Institute of Informatics, Tokyo, Japan, and JST ERATO, Kawarabayashi Project, Japan","institution_ids":["https://openalex.org/I184597095"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080521209","display_name":"Yoshio Okamoto","orcid":"https://orcid.org/0000-0002-9826-7074"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yoshio Okamoto","raw_affiliation_strings":["Department of Communication Engineering and Informatics, University of Electro-Communications, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Communication Engineering and Informatics, University of Electro-Communications, Tokyo, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032398271","display_name":"J\u00e1nos Pach","orcid":"https://orcid.org/0000-0002-2389-2035"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH","HU"],"is_corresponding":false,"raw_author_name":"J\u00e1nos Pach","raw_affiliation_strings":["EPFL, Lausanne, Switzerland and R\u00e9nyi Institute, Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"EPFL, Lausanne, Switzerland and R\u00e9nyi Institute, Budapest, Hungary","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101956627","display_name":"Yuan Tang","orcid":"https://orcid.org/0000-0001-6772-9427"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Tang","raw_affiliation_strings":["Software School, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, P. R. China","Software School, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, P. R. China#TAB#"],"affiliations":[{"raw_affiliation_string":"Software School, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, P. R. China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Software School, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, P. R. China#TAB#","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031520565","display_name":"Takeshi Tokuyama","orcid":"https://orcid.org/0000-0002-9400-8729"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takeshi Tokuyama","raw_affiliation_strings":["Graduate School of Information Sciences, Tohoku University, Sendai, Japan","Graduate School of Information Sciences , Tohoku University , Sendai , Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Information Sciences, Tohoku University, Sendai, Japan","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"Graduate School of Information Sciences , Tohoku University , Sendai , Japan","institution_ids":["https://openalex.org/I201537933"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074370405","display_name":"Sander Verdonschot","orcid":"https://orcid.org/0000-0002-7892-2561"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Sander Verdonschot","raw_affiliation_strings":["School of Computer Science, Carleton University, Ottawa, Canada"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100610986","display_name":"Tianhao Wang","orcid":"https://orcid.org/0000-0002-9017-7947"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianhao Wang","raw_affiliation_strings":["Software School, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, P. R. China","Software School, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, P. R. China#TAB#"],"affiliations":[{"raw_affiliation_string":"Software School, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, P. R. China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Software School, Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, P. R. China#TAB#","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":7,"institutions_distinct_count":13,"corresponding_author_ids":["https://openalex.org/A5038157909"],"corresponding_institution_ids":["https://openalex.org/I67031392"],"apc_list":null,"apc_paid":null,"fwci":1.39338436,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.85327801,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"436","last_page":"443"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.996999979019165,"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"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/antipodal-point","display_name":"Antipodal point","score":0.8408100605010986},{"id":"https://openalex.org/keywords/equilateral-triangle","display_name":"Equilateral triangle","score":0.7344821691513062},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.718311607837677},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.7162504196166992},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6747149229049683},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.6646761298179626},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.6602160334587097},{"id":"https://openalex.org/keywords/midpoint","display_name":"Midpoint","score":0.6475015878677368},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5642117261886597},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5459288358688354},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.5191444754600525},{"id":"https://openalex.org/keywords/convex-polygon","display_name":"Convex polygon","score":0.4297224283218384},{"id":"https://openalex.org/keywords/center-of-mass","display_name":"Center of mass (relativistic)","score":0.42673495411872864},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.42303502559661865},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4060942232608795},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.3372265696525574},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14951643347740173},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12207338213920593},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11022040247917175}],"concepts":[{"id":"https://openalex.org/C70943382","wikidata":"https://www.wikidata.org/wiki/Q505356","display_name":"Antipodal point","level":2,"score":0.8408100605010986},{"id":"https://openalex.org/C146786541","wikidata":"https://www.wikidata.org/wiki/Q157002","display_name":"Equilateral triangle","level":2,"score":0.7344821691513062},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.718311607837677},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.7162504196166992},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6747149229049683},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.6646761298179626},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.6602160334587097},{"id":"https://openalex.org/C34130140","wikidata":"https://www.wikidata.org/wiki/Q1645406","display_name":"Midpoint","level":2,"score":0.6475015878677368},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5642117261886597},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5459288358688354},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.5191444754600525},{"id":"https://openalex.org/C2780034980","wikidata":"https://www.wikidata.org/wiki/Q3259505","display_name":"Convex polygon","level":3,"score":0.4297224283218384},{"id":"https://openalex.org/C36185635","wikidata":"https://www.wikidata.org/wiki/Q17006925","display_name":"Center of mass (relativistic)","level":3,"score":0.42673495411872864},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.42303502559661865},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4060942232608795},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.3372265696525574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14951643347740173},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12207338213920593},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11022040247917175},{"id":"https://openalex.org/C47513753","wikidata":"https://www.wikidata.org/wiki/Q3502299","display_name":"Energy\u2013momentum relation","level":2,"score":0.0},{"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/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"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":1,"locations":[{"id":"doi:10.1145/2582112.2582142","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2582112.2582142","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirtieth annual symposium on Computational geometry","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":10,"referenced_works":["https://openalex.org/W106288804","https://openalex.org/W875084488","https://openalex.org/W1516308076","https://openalex.org/W1547661314","https://openalex.org/W1968861156","https://openalex.org/W1988557746","https://openalex.org/W2033115483","https://openalex.org/W2037502603","https://openalex.org/W2156843639","https://openalex.org/W2530811031"],"related_works":["https://openalex.org/W4293224500","https://openalex.org/W2556176068","https://openalex.org/W1445319306","https://openalex.org/W1566811536","https://openalex.org/W2053288083","https://openalex.org/W2044449173","https://openalex.org/W2205924205","https://openalex.org/W3165507086","https://openalex.org/W2043979935","https://openalex.org/W4300375278"],"abstract_inverted_index":{"Given":[0],"a":[1,5,64],"polygonal":[2],"region":[3,52],"containing":[4,56,106,132],"target":[6],"point":[7],"(which":[8],"we":[9],"assume":[10],"is":[11,15,34,60],"the":[12,26,35,57,70,81,85,91,94,99,107,120,124,133,145],"origin),":[13],"it":[14,59],"not":[16,89],"hard":[17],"to":[18,62],"see":[19],"that":[20,28,73,84,113],"there":[21,109,135],"are":[22,29],"two":[23],"points":[24,112,138],"on":[25,69],"perimeter":[27],"antipodal,":[30],"i.e.,":[31],"whose":[32,139],"midpoint":[33],"origin.":[36,121,146],"We":[37],"prove":[38],"three":[39,111,137],"generalizations":[40],"of":[41,67,77,93,101,126,141],"this":[42],"fact.":[43],"(1)":[44],"For":[45],"any":[46,49,102,127],"polygon":[47],"(or":[48],"bounded":[50,104,129],"closed":[51],"with":[53,80,144],"connected":[54],"boundary)":[55],"origin,":[58,82,108,134],"possible":[61],"place":[63],"given":[65],"set":[66],"weights":[68],"boundary":[71,100],"so":[72],"their":[74],"barycenter":[75],"(center":[76],"mass)":[78],"coincides":[79,143],"provided":[83],"largest":[86],"weight":[87],"does":[88],"exceed":[90],"sum":[92],"other":[95],"weights.":[96],"(2)":[97],"On":[98,123],"3-dimensional":[103,128],"polyhedron":[105,131],"exist":[110,136],"form":[114],"an":[115],"equilateral":[116],"triangle":[117],"centered":[118],"at":[119],"(3)":[122],"1-skeleton":[125],"convex":[130],"center":[140],"mass":[142]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
