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- W4301877124 abstract "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." @default.
- W4301877124 created "2022-10-05" @default.
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- W4301877124 date "2011-07-25" @default.
- W4301877124 modified "2023-10-18" @default.
- W4301877124 title "Reflexive polytopes of higher index and the number 12" @default.
- W4301877124 doi "https://doi.org/10.48550/arxiv.1107.4945" @default.
- W4301877124 hasPublicationYear "2011" @default.
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