{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:06Z","timestamp":1753893846789,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>An abstract polytope is flat if every facet is incident on every vertex. In this paper, we\u00a0prove that no chiral polytope has flat finite regular facets and finite regular vertex-figures.\u00a0We then determine the three smallest non-flat regular polytopes in each rank, and\u00a0use this to show that for $n \\geq 8$, a chiral $n$-polytope has at least $48(n-2)(n-2)!$ flags.<\/jats:p>","DOI":"10.37236\/7070","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:45:21Z","timestamp":1578653121000},"source":"Crossref","is-referenced-by-count":3,"title":["Non-Flat Regular Polytopes and Restrictions on Chiral Polytopes"],"prefix":"10.37236","volume":"24","author":[{"given":"Gabe","family":"Cunningham","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,9,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p59\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p59\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:45:39Z","timestamp":1579218339000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i3p59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,22]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/7070","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,9,22]]},"article-number":"P3.59"}}