{"id":"https://openalex.org/W2117863317","doi":"https://doi.org/10.1007/pl00009393","title":"The Volume as a Metric Invariant of Polyhedra","display_name":"The Volume as a Metric Invariant of Polyhedra","publication_year":1998,"publication_date":"1998-12-01","ids":{"openalex":"https://openalex.org/W2117863317","doi":"https://doi.org/10.1007/pl00009393","mag":"2117863317"},"language":"en","primary_location":{"id":"doi:10.1007/pl00009393","is_oa":true,"landing_page_url":"https://doi.org/10.1007/pl00009393","pdf_url":"https://link.springer.com/content/pdf/10.1007/PL00009393.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/PL00009393.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012474766","display_name":"I. Kh. Sabitov","orcid":null},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"I. Kh. Sabitov","raw_affiliation_strings":["Faculty of Mechanics and Mathematics, Moscow State University,  Moscow, 119899 Russia  matan@nss.msu.su, , , , , , RU","Faculty of Mechanics and Mathematics, Moscow State University,  Moscow, 119899 Russia  matan@nss.msu.su, , RU"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mechanics and Mathematics, Moscow State University,  Moscow, 119899 Russia  matan@nss.msu.su, , , , , , RU","institution_ids":["https://openalex.org/I19880235"]},{"raw_affiliation_string":"Faculty of Mechanics and Mathematics, Moscow State University,  Moscow, 119899 Russia  matan@nss.msu.su, , RU","institution_ids":["https://openalex.org/I19880235"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5012474766"],"corresponding_institution_ids":["https://openalex.org/I19880235"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":8.103,"has_fulltext":true,"cited_by_count":76,"citation_normalized_percentile":{"value":0.97247091,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"20","issue":"4","first_page":"405","last_page":"425"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11870","display_name":"Structural Analysis and Optimization","score":0.9998999834060669,"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":0.9998999834060669,"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/T11737","display_name":"Advanced Materials and Mechanics","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T13267","display_name":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","score":0.9796000123023987,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/polyhedron","display_name":"Polyhedron","score":0.9589482545852661},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7939952611923218},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7047198414802551},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6501373648643494},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5671637058258057},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.49474117159843445},{"id":"https://openalex.org/keywords/volume","display_name":"Volume (thermodynamics)","score":0.48335498571395874},{"id":"https://openalex.org/keywords/bellows","display_name":"Bellows","score":0.4286058843135834},{"id":"https://openalex.org/keywords/minimal-volume","display_name":"Minimal volume","score":0.4155583381652832},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2163974642753601}],"concepts":[{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.9589482545852661},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7939952611923218},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7047198414802551},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6501373648643494},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5671637058258057},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.49474117159843445},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.48335498571395874},{"id":"https://openalex.org/C2779410321","wikidata":"https://www.wikidata.org/wiki/Q208103","display_name":"Bellows","level":2,"score":0.4286058843135834},{"id":"https://openalex.org/C121208196","wikidata":"https://www.wikidata.org/wiki/Q17103928","display_name":"Minimal volume","level":5,"score":0.4155583381652832},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2163974642753601},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/pl00009393","is_oa":true,"landing_page_url":"https://doi.org/10.1007/pl00009393","pdf_url":"https://link.springer.com/content/pdf/10.1007/PL00009393.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"Discrete & Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/pl00009393","is_oa":true,"landing_page_url":"https://doi.org/10.1007/pl00009393","pdf_url":"https://link.springer.com/content/pdf/10.1007/PL00009393.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320313621","display_name":"Russian Foundation for Fundamental Investigations","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2117863317.pdf","grobid_xml":"https://content.openalex.org/works/W2117863317.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W56456726","https://openalex.org/W333982791","https://openalex.org/W1494380125","https://openalex.org/W2025461635","https://openalex.org/W2035591777","https://openalex.org/W2318985534","https://openalex.org/W2731598242","https://openalex.org/W4236810476","https://openalex.org/W4255107382"],"related_works":["https://openalex.org/W2315538653","https://openalex.org/W2325260228","https://openalex.org/W2350729696","https://openalex.org/W2365467715","https://openalex.org/W2347886893","https://openalex.org/W4299961962","https://openalex.org/W2399282594","https://openalex.org/W4297950433","https://openalex.org/W2558235681","https://openalex.org/W4299416706"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-25T08:17:42.794288","created_date":"2025-10-10T00:00:00"}