  The Peterson variety is a remarkable variety introduced by Dale Peterson to
describe the quantum cohomology rings of all the partial flag varieties. The
rational cohomology ring of the Peterson variety is known to be isomorphic to
that of a particular toric orbifold which naturally arises from the given root
system. In this paper, we show that it is not an accidental algebraic
coincidence; we construct an explicit morphism from the Peterson variety to the
toric orbifold which induces a ring isomorphism between their rational
cohomology rings.
