{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:26:29Z","timestamp":1759335989522,"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>We introduce reflexive polytopes of index $l$ as a natural generalisation of the notion of a reflexive polytope of index $1$. These $l$-reflexive polytopes also appear as dual pairs. In dimension two we show that they arise from reflexive polygons via a change of the underlying lattice. This allows us to efficiently classify all isomorphism classes of $l$-reflexive polygons up to index $200$. As another application, we show that any reflexive polygon of arbitrary index satisfies the famous \"number $12$\" property. This is a new, infinite class of lattice polygons possessing this property, and extends the previously known sixteen instances. The number $12$ property also holds more generally for $l$-reflexive non-convex or self-intersecting polygonal loops. We conclude by discussing higher-dimensional examples and open questions.<\/jats:p>","DOI":"10.37236\/2366","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:25:43Z","timestamp":1578713143000},"source":"Crossref","is-referenced-by-count":7,"title":["Reflexive Polytopes of Higher Index and the Number 12"],"prefix":"10.37236","volume":"19","author":[{"given":"Alexander M.","family":"Kasprzyk","sequence":"first","affiliation":[]},{"given":"Benjamin","family":"Nill","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,7,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i3p9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i3p9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:32:34Z","timestamp":1579300354000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i3p9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,7,19]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2012,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/2366","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,7,19]]},"article-number":"P9"}}