{"id":"https://openalex.org/W2047205254","doi":"https://doi.org/10.1007/s00454-007-1342-7","title":"Four-Dimensional Regular Polyhedra","display_name":"Four-Dimensional Regular Polyhedra","publication_year":2007,"publication_date":"2007-09-01","ids":{"openalex":"https://openalex.org/W2047205254","doi":"https://doi.org/10.1007/s00454-007-1342-7","mag":"2047205254"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-007-1342-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-007-1342-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-007-1342-7.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 &amp; 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/s00454-007-1342-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069372898","display_name":"Peter McMullen","orcid":"https://orcid.org/0000-0001-8444-8045"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Peter McMullen","raw_affiliation_strings":["Department of Mathematics, University College London, Gower Street, London WC1E 6BT, England","Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University College London, Gower Street, London WC1E 6BT, England","institution_ids":["https://openalex.org/I45129253"]},{"raw_affiliation_string":"Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England","institution_ids":["https://openalex.org/I45129253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069372898"],"corresponding_institution_ids":["https://openalex.org/I45129253"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.0644,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.73631124,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"38","issue":"2","first_page":"355","last_page":"387"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9983999729156494,"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/T10849","display_name":"Finite Group Theory Research","score":0.9983999729156494,"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/T11797","display_name":"graph theory and CDMA systems","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10374","display_name":"Advanced Graph Theory Research","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.9074170589447021},{"id":"https://openalex.org/keywords/coxeter-group","display_name":"Coxeter group","score":0.8060300350189209},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7832573652267456},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7638065218925476},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.7310516238212585},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6380398869514465},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5009236335754395},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.49950718879699707},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.49160417914390564},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.43369054794311523},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4313719868659973},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17073971033096313},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.14659500122070312},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07645556330680847}],"concepts":[{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.9074170589447021},{"id":"https://openalex.org/C143669375","wikidata":"https://www.wikidata.org/wiki/Q7874246","display_name":"Coxeter group","level":2,"score":0.8060300350189209},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7832573652267456},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7638065218925476},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7310516238212585},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6380398869514465},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5009236335754395},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.49950718879699707},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.49160417914390564},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.43369054794311523},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4313719868659973},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17073971033096313},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.14659500122070312},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07645556330680847},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-007-1342-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-007-1342-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-007-1342-7.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 &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:104978","is_oa":false,"landing_page_url":"http://discovery.ucl.ac.uk/104978/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"   DISCRETE COMPUT GEOM , 38  (2)   355 - 387.   (2007)      ","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s00454-007-1342-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-007-1342-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-007-1342-7.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 &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2047205254.pdf","grobid_xml":"https://content.openalex.org/works/W2047205254.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W51037165","https://openalex.org/W1654930094","https://openalex.org/W1964676217","https://openalex.org/W1967444329","https://openalex.org/W1984435882","https://openalex.org/W1985215525","https://openalex.org/W2000411577","https://openalex.org/W2020641847","https://openalex.org/W2062938993","https://openalex.org/W2079219714","https://openalex.org/W2087666661","https://openalex.org/W2104502278","https://openalex.org/W2140504886","https://openalex.org/W2158834265","https://openalex.org/W2330471604","https://openalex.org/W2333820330","https://openalex.org/W2386238139","https://openalex.org/W2573857691","https://openalex.org/W2586829639","https://openalex.org/W2596121519","https://openalex.org/W2610447370","https://openalex.org/W4213089498","https://openalex.org/W4243311420"],"related_works":["https://openalex.org/W2099246938","https://openalex.org/W2004058166","https://openalex.org/W2143716978","https://openalex.org/W4280544053","https://openalex.org/W940482830","https://openalex.org/W1996058844","https://openalex.org/W2034907509","https://openalex.org/W1982460031","https://openalex.org/W2009773457","https://openalex.org/W3157359326"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
