{"id":"https://openalex.org/W2013577490","doi":"https://doi.org/10.1307/mmj/1028998436","title":"On polyhedra in spaces of constant curvature.","display_name":"On polyhedra in spaces of constant curvature.","publication_year":1960,"publication_date":"1960-01-01","ids":{"openalex":"https://openalex.org/W2013577490","doi":"https://doi.org/10.1307/mmj/1028998436","mag":"2013577490"},"language":"en","primary_location":{"id":"doi:10.1307/mmj/1028998436","doi":"https://doi.org/10.1307/mmj/1028998436","is_oa":true,"landing_page_url":"https://doi.org/10.1307/mmj/1028998436","pdf_url":"https://projecteuclid.org/journals/michigan-mathematical-journal/volume-7/issue-3/On-polyhedra-in-spaces-of-constant-curvature/10.1307/mmj/1028998436.pdf","source":{"id":"https://openalex.org/S177543170","display_name":"The Michigan Mathematical Journal","issn_l":"0026-2285","issn":["0026-2285","1945-2365"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Michigan Mathematical Journal","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/michigan-mathematical-journal/volume-7/issue-3/On-polyhedra-in-spaces-of-constant-curvature/10.1307/mmj/1028998436.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016519872","display_name":"Herbert Knothe","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Herbert Knothe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5016519872"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17343173,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":"3","first_page":"251","last_page":"255"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.7080000042915344,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.7080000042915344,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.16110000014305115,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.030899999663233757,"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/polyhedra","display_name":"polyhedra","score":0.9959999918937683},{"id":"https://openalex.org/keywords/spaces-of-constant-curvature","display_name":"spaces of constant curvature","score":0.9399999976158142},{"id":"https://openalex.org/keywords/spherical-geometry","display_name":"spherical geometry","score":0.5889999866485596},{"id":"https://openalex.org/keywords/hyperbolic-geometry","display_name":"hyperbolic geometry","score":0.9829999804496765},{"id":"https://openalex.org/keywords/polyhedral-geometry","display_name":"polyhedral geometry","score":0.550000011920929}],"concepts":[{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.9014384746551514},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.700901985168457},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6798648834228516},{"id":"https://openalex.org/C2779668893","wikidata":"https://www.wikidata.org/wiki/Q2250422","display_name":"Constant curvature","level":3,"score":0.6165440678596497},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5689923763275146},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.43498462438583374},{"id":"https://openalex.org/C161223928","wikidata":"https://www.wikidata.org/wiki/Q3775868","display_name":"Center of curvature","level":4,"score":0.43138113617897034},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.3999137282371521},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37109655141830444},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09399473667144775},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1307/mmj/1028998436","doi":"https://doi.org/10.1307/mmj/1028998436","is_oa":true,"landing_page_url":"https://doi.org/10.1307/mmj/1028998436","pdf_url":"https://projecteuclid.org/journals/michigan-mathematical-journal/volume-7/issue-3/On-polyhedra-in-spaces-of-constant-curvature/10.1307/mmj/1028998436.pdf","source":{"id":"https://openalex.org/S177543170","display_name":"The Michigan Mathematical Journal","issn_l":"0026-2285","issn":["0026-2285","1945-2365"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Michigan Mathematical Journal","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.mmj/1028998436","doi":null,"is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.mmj/1028998436","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1307/mmj/1028998436","doi":"https://doi.org/10.1307/mmj/1028998436","is_oa":true,"landing_page_url":"https://doi.org/10.1307/mmj/1028998436","pdf_url":"https://projecteuclid.org/journals/michigan-mathematical-journal/volume-7/issue-3/On-polyhedra-in-spaces-of-constant-curvature/10.1307/mmj/1028998436.pdf","source":{"id":"https://openalex.org/S177543170","display_name":"The Michigan Mathematical Journal","issn_l":"0026-2285","issn":["0026-2285","1945-2365"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Michigan Mathematical Journal","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2013577490.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4256447176","https://openalex.org/W1998264400","https://openalex.org/W2313436308","https://openalex.org/W2057853563","https://openalex.org/W2608252313","https://openalex.org/W4254442836","https://openalex.org/W2027489848","https://openalex.org/W2003338909","https://openalex.org/W4411072780","https://openalex.org/W2325025329"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-10-21T09:56:26.102985","created_date":"2016-06-24T00:00:00"}