{"id":"https://openalex.org/W2065353776","doi":"https://doi.org/10.1007/s10998-006-0023-2","title":"Typical faces of extremal polytopes with respect to a thin three-dimensional shell","display_name":"Typical faces of extremal polytopes with respect to a thin three-dimensional shell","publication_year":2006,"publication_date":"2006-09-01","ids":{"openalex":"https://openalex.org/W2065353776","doi":"https://doi.org/10.1007/s10998-006-0023-2","mag":"2065353776"},"language":"en","primary_location":{"id":"doi:10.1007/s10998-006-0023-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10998-006-0023-2","pdf_url":null,"source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-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/A5017014622","display_name":"K\u00e1roly J. B\u00f6r\u00f6czky","orcid":"https://orcid.org/0000-0002-2882-4496"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]},{"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"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"K\u00e1roly B\u00f6r\u00f6czky","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics  & Department of Geometry, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/c H-1117 Budapest, Hungary & H--1364, Budapest, P.O. Box 127, Hungary","Department of Geometry, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/c H-1117 Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics  & Department of Geometry, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/c H-1117 Budapest, Hungary & H--1364, Budapest, P.O. Box 127, Hungary","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I106118109"]},{"raw_affiliation_string":"Department of Geometry, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/c H-1117 Budapest, Hungary","institution_ids":["https://openalex.org/I106118109"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017014622","display_name":"K\u00e1roly J. B\u00f6r\u00f6czky","orcid":"https://orcid.org/0000-0002-2882-4496"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]},{"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"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"K\u00e1roly B\u00f6r\u00f6czky Jr.","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics  & Department of Geometry, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/c H-1117 Budapest, Hungary & H--1364, Budapest, P.O. Box 127, Hungary","Department of Geometry, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/c H-1117 Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics  & Department of Geometry, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/c H-1117 Budapest, Hungary & H--1364, Budapest, P.O. Box 127, Hungary","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I106118109"]},{"raw_affiliation_string":"Department of Geometry, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/c H-1117 Budapest, Hungary","institution_ids":["https://openalex.org/I106118109"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086284776","display_name":"Gergely Wintsche","orcid":"https://orcid.org/0000-0002-4426-0424"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Gergely Wintsche","raw_affiliation_strings":["Department of Geometry, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/c H-1117 Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"Department of Geometry, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/c H-1117 Budapest, Hungary","institution_ids":["https://openalex.org/I106118109"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5017014622"],"corresponding_institution_ids":["https://openalex.org/I106118109","https://openalex.org/I127817813"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.4542,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.61964518,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"53","issue":"1-2","first_page":"83","last_page":"102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9998999834060669,"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/T11822","display_name":"Analytic and geometric function theory","score":0.9944999814033508,"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":0.9915000200271606,"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/mathematics","display_name":"Mathematics","score":0.7984806299209595},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7320113182067871},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.679746150970459},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.676182746887207},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6356777548789978},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.5646846294403076},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.4991767406463623},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.43313974142074585},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.4139559864997864},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.1958640217781067}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7984806299209595},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7320113182067871},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.679746150970459},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.676182746887207},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6356777548789978},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.5646846294403076},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.4991767406463623},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.43313974142074585},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4139559864997864},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.1958640217781067},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10998-006-0023-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10998-006-0023-2","pdf_url":null,"source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W119189535","https://openalex.org/W1571966798","https://openalex.org/W1606263708","https://openalex.org/W1970966506","https://openalex.org/W2042419499","https://openalex.org/W2092853349","https://openalex.org/W2159258685"],"related_works":["https://openalex.org/W2091689278","https://openalex.org/W3120597765","https://openalex.org/W4287712648","https://openalex.org/W3043508332","https://openalex.org/W2387072865","https://openalex.org/W4287022798","https://openalex.org/W2804455714","https://openalex.org/W1530081058","https://openalex.org/W3202391809","https://openalex.org/W3042052879"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}