Abstract & Overview
It is well known that there are 16 two-dimensional reflexive polytopes up to lattice isomorphism. One can check directly from the list that the number of lattice points on the boundary of such a polytope plus the number of lattice points on the boundary of the dual polytope is always 12. It turns out that two-dimensional reflexive polytopes correspond to certain relations of two generators A and B of SL 2(ℤ) of length 12. We generalize this correspondence to reflexive configurations with winding number w and relations of length 12w.