As is well known, each toric variety corresponds to a fan. Moreover, each fan corresponding to smooth toric Fano variety can be interpreted as a polytope, so-called a smooth Fano polytope.
In this talk, we will introduce two equivalent relations among smooth Fano polytopes
(equivalently, among smooth toric Fano varieties), which are F-equivalence and I-equivalence,
and discuss some equivalent classes for smooth Fano polytopes.