  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 $B_\infty$.
