Bull. Korean Math. Soc. Published online April 8, 2021
DongSeon Hwang and Yeonsu Kim
Abstract : We introduce the notion of barycentric transformation of Fano polytopes, from which we can assign a certain type to each Fano polytope. The type can be viewed as a measure of the extent to which the given Fano polytope is close to be K\"ahler-Einstein. In particular, we expect that every K\"ahler-Einstein or symmetric Fano polytope is of type B_\infty. We verify this expectation for some low dimensional cases. We emphasize that for a Fano polytope X of dimension 1, 3 or 5, X is K\"ahler-Einstein if and only if it is of type B_\infty.