{"id":"https://openalex.org/W4394643205","doi":"https://doi.org/10.48550/arxiv.cs/0407063","title":"Unfolding Smooth Prismatoids","display_name":"Unfolding Smooth Prismatoids","publication_year":2004,"publication_date":"2004-07-28","ids":{"openalex":"https://openalex.org/W4394643205","doi":"https://doi.org/10.48550/arxiv.cs/0407063"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:cs/0407063","is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/0407063","pdf_url":"https://arxiv.org/pdf/cs/0407063","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/cs/0407063","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076326702","display_name":"Nadia M. Benbernou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Benbernou, Nadia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066368701","display_name":"Patricia Cahn","orcid":"https://orcid.org/0000-0002-2834-0897"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cahn, Patricia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5025667097","display_name":"Joseph O\u2019Rourke","orcid":"https://orcid.org/0000-0001-5844-506X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"O'Rourke, Joseph","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"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":0.3027999997138977,"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":0.3027999997138977,"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":0.1931000053882599,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.17069999873638153,"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/business","display_name":"Business","score":0.32869797945022583}],"concepts":[{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.32869797945022583}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:cs/0407063","is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/0407063","pdf_url":"https://arxiv.org/pdf/cs/0407063","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},{"id":"pmh:oai:scholarworks.smith.edu:csc_facpubs-1054","is_oa":true,"landing_page_url":"https://scholarworks.smith.edu/csc_facpubs/46","pdf_url":"https://scholarworks.smith.edu/csc_facpubs/46","source":{"id":"https://openalex.org/S4377196392","display_name":"Smith ScholarWorks (Smith College)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I202524275","host_organization_name":"Smith College","host_organization_lineage":["https://openalex.org/I202524275"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computer Science: Faculty Publications","raw_type":"text"},{"id":"doi:10.48550/arxiv.cs/0407063","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.cs/0407063","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:cs/0407063","is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/0407063","pdf_url":"https://arxiv.org/pdf/cs/0407063","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2765153054","https://openalex.org/W2596173151","https://openalex.org/W3213789065","https://openalex.org/W3080576469","https://openalex.org/W4231340554","https://openalex.org/W1491839574","https://openalex.org/W2931838652","https://openalex.org/W3168296622","https://openalex.org/W4307515305"],"abstract_inverted_index":{"We":[0],"define":[1],"a":[2,27,59],"notion":[3],"for":[4,61,66],"unfolding":[5],"smooth,":[6],"ruled":[7],"surfaces,":[8],"and":[9,45],"prove":[10],"that":[11],"every":[12],"smooth":[13,20,62],"prismatoid":[14],"(the":[15],"convex":[16],"hull":[17],"of":[18,52],"two":[19],"curves":[21],"lying":[22],"in":[23],"parallel":[24],"planes),":[25],"has":[26],"nonoverlapping":[28],"\"volcano":[29],"unfolding.\"":[30],"These":[31],"unfoldings":[32],"keep":[33],"the":[34,38,43,47,50],"base":[35],"intact,":[36],"unfold":[37],"sides":[39],"outward,":[40],"splayed":[41],"around":[42],"base,":[44],"attach":[46],"top":[48],"to":[49],"tip":[51],"some":[53],"side":[54],"rib.":[55],"Our":[56],"result":[57],"answers":[58],"question":[60],"prismatoids":[63,68],"whose":[64],"analog":[65],"polyhedral":[67],"remains":[69],"unsolved.":[70]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}