{"id":"https://openalex.org/W2346545628","doi":"https://doi.org/10.1137/15m1054833","title":"Prestress Stability of Triangulated Convex Polytopes and Universal Second-Order Rigidity","display_name":"Prestress Stability of Triangulated Convex Polytopes and Universal Second-Order Rigidity","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2346545628","doi":"https://doi.org/10.1137/15m1054833","mag":"2346545628"},"language":"en","primary_location":{"id":"doi:10.1137/15m1054833","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1054833","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1510.04185","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043799032","display_name":"Robert Connelly","orcid":"https://orcid.org/0000-0003-3757-8124"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert Connelly","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5012875116","display_name":"Steven J. Gortler","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steven J. Gortler","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00231704,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"31","issue":"4","first_page":"2735","last_page":"2753"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11870","display_name":"Structural Analysis and Optimization","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11870","display_name":"Structural Analysis and Optimization","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9926000237464905,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9876999855041504,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rigidity","display_name":"Rigidity (electromagnetism)","score":0.7787064909934998},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6784324645996094},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6633934378623962},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.464366614818573},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43492555618286133},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4219302535057068},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41024279594421387},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.307595431804657},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2626791000366211},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.24062243103981018},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.19599157571792603},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.09079506993293762}],"concepts":[{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.7787064909934998},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6784324645996094},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6633934378623962},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.464366614818573},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43492555618286133},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4219302535057068},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41024279594421387},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.307595431804657},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2626791000366211},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.24062243103981018},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.19599157571792603},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.09079506993293762},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/15m1054833","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1054833","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1510.04185","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.04185","pdf_url":"https://arxiv.org/pdf/1510.04185","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,"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":"mag:2346545628","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1510.04185v1","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,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1510.04185","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1510.04185","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1510.04185","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.04185","pdf_url":"https://arxiv.org/pdf/1510.04185","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,"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":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.47999998927116394}],"awards":[{"id":"https://openalex.org/G3193980100","display_name":"FRG: Collaborative Research: Stability of Structures Large and Small","funder_award_id":"1564473","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6622191306","display_name":null,"funder_award_id":"DMS-1564473","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6624825394","display_name":null,"funder_award_id":"DMS-1564493","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2346545628.pdf","grobid_xml":"https://content.openalex.org/works/W2346545628.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W324457701","https://openalex.org/W624923763","https://openalex.org/W1481113074","https://openalex.org/W1530933630","https://openalex.org/W1964602626","https://openalex.org/W1964858253","https://openalex.org/W1971255824","https://openalex.org/W1974956622","https://openalex.org/W2000214666","https://openalex.org/W2010786313","https://openalex.org/W2019234444","https://openalex.org/W2019651569","https://openalex.org/W2027524385","https://openalex.org/W2052737601","https://openalex.org/W2088080526","https://openalex.org/W2104296611","https://openalex.org/W2110167134","https://openalex.org/W2166161233","https://openalex.org/W2166522594","https://openalex.org/W2553598374","https://openalex.org/W4210394880","https://openalex.org/W4252572845"],"related_works":["https://openalex.org/W2735102567","https://openalex.org/W2472099489","https://openalex.org/W2963742618","https://openalex.org/W2014016116","https://openalex.org/W2952448168","https://openalex.org/W178347475","https://openalex.org/W2949462405","https://openalex.org/W2175993482","https://openalex.org/W2963937081","https://openalex.org/W2048802156","https://openalex.org/W2965387605","https://openalex.org/W2078174180","https://openalex.org/W2507648344","https://openalex.org/W2756266626","https://openalex.org/W137282128","https://openalex.org/W2091746789","https://openalex.org/W2075599725","https://openalex.org/W1984034063","https://openalex.org/W1702184388","https://openalex.org/W1516466202"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,11],"universal":[3,7],"second-order":[4],"rigidity":[5],"implies":[6],"prestress":[8,22],"stability":[9],"and":[10],"triangulated":[12],"convex":[13],"polytopes":[14],"in":[15],"three-space":[16],"(with":[17],"holes":[18],"appropriately":[19],"positioned)":[20],"are":[21],"stable.":[23]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
