Reflexive Polytopes of Higher Index and the Number 12

@article{Kasprzyk2012ReflexivePO,
  title={Reflexive Polytopes of Higher Index and the Number 12},
  author={A. Kasprzyk and Benjamin Nill},
  journal={Electron. J. Comb.},
  year={2012},
  volume={19},
  pages={P9}
}
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… Expand
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