Polytopes, Skeleta and Homological Mirror Symmetry at the Limit

A function in n variables whose Newton polytope is reflexive
defines an affine Calabi-Yau hypersurface X which appears at
the large volume limit in mirror symmetry.

Given this combinatorial data, I will define a CW complex
which should be thought of as the Lagrangian skeleton of the
hypersurface.  (The construction is intuitive to tropical
geometers.)  It is homotopy equivalent to X.
I will also define a category which is equivalent to the category
of vector bundles of the large complex mirror, and conjecturally
equivalent to the Fukaya category of X.

I will focus on pictures and examples.