{"id":"https://openalex.org/W2062984786","doi":"https://doi.org/10.1007/s00454-004-1140-4","title":"The Et-Construction for Lattices, Spheres and Polytopes","display_name":"The Et-Construction for Lattices, Spheres and Polytopes","publication_year":2004,"publication_date":"2004-08-23","ids":{"openalex":"https://openalex.org/W2062984786","doi":"https://doi.org/10.1007/s00454-004-1140-4","mag":"2062984786"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-004-1140-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-004-1140-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1140-4.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/s00454-004-1140-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075556519","display_name":"Andreas Paffenholz","orcid":"https://orcid.org/0000-0001-9718-523X"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Andreas Paffenholz","raw_affiliation_strings":["Institut f\u00fcr Mathematik, MA 6-2,\n Technische Universit\u00e4t Berlin, D-10623 Berlin, Germany","Institut f\u00fcr Mathematik, MA 6-2,#N# Technische Universit\u00e4t Berlin, D-10623 Berlin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, MA 6-2,\n Technische Universit\u00e4t Berlin, D-10623 Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik, MA 6-2,#N# Technische Universit\u00e4t Berlin, D-10623 Berlin","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110110465","display_name":"G\ufffdnter M. Ziegler","orcid":null},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"G\ufffdnter M. Ziegler","raw_affiliation_strings":["Institut f\u00fcr Mathematik, MA 6-2,\n Technische Universit\u00e4t Berlin, D-10623 Berlin, Germany","Institut f\u00fcr Mathematik, MA 6-2,#N# Technische Universit\u00e4t Berlin, D-10623 Berlin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, MA 6-2,\n Technische Universit\u00e4t Berlin, D-10623 Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik, MA 6-2,#N# Technische Universit\u00e4t Berlin, D-10623 Berlin","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075556519","https://openalex.org/A5110110465"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":5.6849,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.96575342,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"32","issue":"4","first_page":"601","last_page":"621"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9832000136375427,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.8946508765220642},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7669415473937988},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7327593564987183},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6633512377738953},{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.6447329521179199},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5905767679214478},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"Simplicial complex","score":0.5165897607803345},{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.5144624710083008},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.4882228672504425},{"id":"https://openalex.org/keywords/face","display_name":"Face (sociological concept)","score":0.4611172676086426},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20947036147117615},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.1738521158695221},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12984168529510498},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11178353428840637},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06285342574119568}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8946508765220642},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7669415473937988},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7327593564987183},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6633512377738953},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.6447329521179199},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5905767679214478},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.5165897607803345},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.5144624710083008},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4882228672504425},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.4611172676086426},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20947036147117615},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.1738521158695221},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12984168529510498},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11178353428840637},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06285342574119568},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","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},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00454-004-1140-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-004-1140-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1140-4.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:CiteSeerX.psu:10.1.1.14.2266","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.14.2266","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.math.tu-berlin.de/pub/combi/ziegler/WWW/89et.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.214.8414","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.8414","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tu-berlin.de/~paffenho/preprints/et.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.235.5916","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.5916","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0304492v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.235.9820","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.9820","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0304492v2.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/s00454-004-1140-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-004-1140-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1140-4.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":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.7200000286102295}],"awards":[{"id":"https://openalex.org/G3450025437","display_name":null,"funder_award_id":"FZT86","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7025150052","display_name":null,"funder_award_id":"GRK 588/2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334763","display_name":"Leibniz-Gemeinschaft","ror":"https://ror.org/01n6r0e97"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2062984786.pdf","grobid_xml":"https://content.openalex.org/works/W2062984786.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W100715979","https://openalex.org/W186032282","https://openalex.org/W608832534","https://openalex.org/W1481113074","https://openalex.org/W1494782546","https://openalex.org/W1565240535","https://openalex.org/W1597196612","https://openalex.org/W2013121652","https://openalex.org/W2041186059","https://openalex.org/W2054009182","https://openalex.org/W2076040982","https://openalex.org/W2105776550","https://openalex.org/W2123323408","https://openalex.org/W2162775739","https://openalex.org/W2171484299","https://openalex.org/W2334336952","https://openalex.org/W2971330320","https://openalex.org/W3015754474","https://openalex.org/W4288935732","https://openalex.org/W4300302225","https://openalex.org/W4388295056","https://openalex.org/W6606642502","https://openalex.org/W6637281795","https://openalex.org/W6697549010"],"related_works":["https://openalex.org/W4280529077","https://openalex.org/W2507185596","https://openalex.org/W1493684871","https://openalex.org/W4286224459","https://openalex.org/W2886567582","https://openalex.org/W4287022798","https://openalex.org/W2884061808","https://openalex.org/W2901329027","https://openalex.org/W2958361321","https://openalex.org/W2243080753"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}