In this talk, I will discuss the combinatorics of the affine Grassmannian, the affine flag variety and the central degeneration, with an emphasis on some convex polytopes involved. The affine Grassmannian and affine flag variety are the infinite-dimensional analogs of the ordinary Grassmannian and flag variety. The central degeneration is the degeneration that shows up in local models of Shimura varieties and Gaitsgory's central sheaves. Our convex polytopes are the moment polytopes of some schemes, and turn out to be special cases of the alcoved polytopes studied by Lam and Postnikov. Speaker(s): Qiao Zhou (UC Berkeley)