@article {IOPORT.06098351,
    author       = {Kasprzyk, Alexander M. and Nill, Benjamin},
    title        = {Reflexive polytopes of higher index and the number 12.},
    year         = {2012},
    journal      = {The Electronic Journal of Combinatorics [electronic only]},
    volume       = {19},
    number       = {3},
    issn         = {1077-8926},
    pages        = {Research Paper P9, 18 p., electronic only},
    publisher    = {Prof. Andr\'e K\"undgen, Deptartment of Mathematics, California State University San Marcos, San Marcos, CA},
    abstract     = {Summary: 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.},
    identifier   = {06098351},
}