{"id":"https://openalex.org/W2017443311","doi":"https://doi.org/10.1007/s00454-010-9304-x","title":"Upper Bound on the Packing Density of Regular Tetrahedra and Octahedra","display_name":"Upper Bound on the Packing Density of Regular Tetrahedra and Octahedra","publication_year":2010,"publication_date":"2010-10-13","ids":{"openalex":"https://openalex.org/W2017443311","doi":"https://doi.org/10.1007/s00454-010-9304-x","mag":"2017443311"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-010-9304-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-010-9304-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-010-9304-x.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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-010-9304-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110660348","display_name":"Simon Gravel","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Simon Gravel","raw_affiliation_strings":["Department of Genetics, Stanford University School of Medicine, Stanford, CA, 94305-5120, USA","Stanford University School of Medicine, Department of Genetics, 94305-5120, Stanford, CA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Genetics, Stanford University School of Medicine, Stanford, CA, 94305-5120, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Stanford University School of Medicine, Department of Genetics, 94305-5120, Stanford, CA, USA#TAB#","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009624693","display_name":"Veit Elser","orcid":"https://orcid.org/0000-0002-6961-4778"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Veit Elser","raw_affiliation_strings":["Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, 14853-2501, USA","Cornell University, Laboratory of Atomic and Solid State Physics, 14853-2501, Ithaca, NY, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, 14853-2501, USA","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Cornell University, Laboratory of Atomic and Solid State Physics, 14853-2501, Ithaca, NY, USA#TAB#","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060735452","display_name":"Yoav Kallus","orcid":"https://orcid.org/0000-0002-1968-4671"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yoav Kallus","raw_affiliation_strings":["Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, 14853-2501, USA","Cornell University, Laboratory of Atomic and Solid State Physics, 14853-2501, Ithaca, NY, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, 14853-2501, USA","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Cornell University, Laboratory of Atomic and Solid State Physics, 14853-2501, Ithaca, NY, USA#TAB#","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110660348"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.6353,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.67218917,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"46","issue":"4","first_page":"799","last_page":"818"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11737","display_name":"Advanced Materials and Mechanics","score":0.9958000183105469,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.9474582672119141},{"id":"https://openalex.org/keywords/octahedron","display_name":"Octahedron","score":0.6447381377220154},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6134265065193176},{"id":"https://openalex.org/keywords/sphere-packing","display_name":"Sphere packing","score":0.5961518883705139},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.5580736994743347},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48212575912475586},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4785673916339874},{"id":"https://openalex.org/keywords/packing-problems","display_name":"Packing problems","score":0.47770336270332336},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.46020716428756714},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4483977258205414},{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.4465102553367615},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.3725582957267761},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.33090245723724365},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2094269096851349},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14604023098945618},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.13951635360717773},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1244838535785675},{"id":"https://openalex.org/keywords/crystal-structure","display_name":"Crystal structure","score":0.11402538418769836}],"concepts":[{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.9474582672119141},{"id":"https://openalex.org/C198819137","wikidata":"https://www.wikidata.org/wiki/Q188884","display_name":"Octahedron","level":3,"score":0.6447381377220154},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6134265065193176},{"id":"https://openalex.org/C183893376","wikidata":"https://www.wikidata.org/wiki/Q900117","display_name":"Sphere packing","level":2,"score":0.5961518883705139},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.5580736994743347},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48212575912475586},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4785673916339874},{"id":"https://openalex.org/C130253271","wikidata":"https://www.wikidata.org/wiki/Q3851477","display_name":"Packing problems","level":2,"score":0.47770336270332336},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.46020716428756714},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4483977258205414},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.4465102553367615},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.3725582957267761},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.33090245723724365},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2094269096851349},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14604023098945618},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.13951635360717773},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1244838535785675},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.11402538418769836},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-010-9304-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-010-9304-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-010-9304-x.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"},{"id":"pmh:oai:arXiv.org:1008.2830","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1008.2830","pdf_url":"https://arxiv.org/pdf/1008.2830","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":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/s00454-010-9304-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-010-9304-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-010-9304-x.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":[{"id":"https://metadata.un.org/sdg/11","score":0.6200000047683716,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2017443311.pdf","grobid_xml":"https://content.openalex.org/works/W2017443311.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1818132603","https://openalex.org/W1968836887","https://openalex.org/W1981804590","https://openalex.org/W1994442402","https://openalex.org/W2016323043","https://openalex.org/W2034430120","https://openalex.org/W2053911766","https://openalex.org/W2072920688","https://openalex.org/W2083379047","https://openalex.org/W2138706582","https://openalex.org/W2142823388","https://openalex.org/W2153489159","https://openalex.org/W2159130720","https://openalex.org/W2167385678","https://openalex.org/W2321267061","https://openalex.org/W3098845077","https://openalex.org/W3100999267","https://openalex.org/W3105847690","https://openalex.org/W4211043430"],"related_works":["https://openalex.org/W4239526988","https://openalex.org/W1802456315","https://openalex.org/W4235007892","https://openalex.org/W2396049332","https://openalex.org/W2922863847","https://openalex.org/W2186513065","https://openalex.org/W2518606980","https://openalex.org/W139605340","https://openalex.org/W2582711371","https://openalex.org/W1999537217"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}