  A prismatoid is a polytope with all its vertices contained in two parallel
facets, called its bases. Its width is the number of steps needed to go from
one base to the other in the dual graph. The first author recently showed that
the existence of counter-examples to the Hirsch conjecture is equivalent to
that of $d$-prismatoids of width larger than $d$, and constructed such
prismatoids in dimension five. Here we show that the same is impossible in
dimension four. This is proved by looking at the pair of graph embeddings on a
2-sphere that arise from the normal fans of the two bases.
