LDP polygons and the number 12 revisited

Abstract

We give a combinatorial proof of a lattice point identity involving a lattice polygon and its dual, generalizing the formula $area(\Delta )+area({\Delta }^{\ast })=6$ for reflexive $\Delta$. The identity is equivalent to the stringy Libgober-Wood identity for toric log del Pezzo surfaces.

20 pages, 8 figures