{"id":"https://openalex.org/keywords/polytopes","display_name":"polytopes","description":"Polytopes are geometric objects in any number of dimensions bounded by flat faces, generalizing polygons and polyhedra.","display_name_alternatives":["polytope"],"ids":{"openalex":"https://openalex.org/keywords/polytopes","wikidata":"https://www.wikidata.org/wiki/Q747980"},"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.262,"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":0.262,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.1014,"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"}}],"works_count":5262,"cited_by_count":60052,"works_api_url":"https://api.openalex.org/works?filter=keywords.id:keywords/polytopes","updated_date":"2026-10-22T04:07:25","created_date":"2026-09-30T00:00:00"}