  The higher Bruhat order is a poset of cubical tilings of a cyclic zonotope
whose covering relations are cubical flips. For a 2-dimensional zonotope, the
higher Bruhat order is isomorphic to a poset on commutation classes of reduced
words for the longest element of a type A Coxeter system. For this case, we
prove that the noncontractible intervals are in natural correspondence with the
zonogonal tilings of a zonogon. Our proof uses some tools developed by Felsner
and Weil to show that the two standard orderings on the rhombic tilings of a
zonogon are identical.
