  A geometric graph \G is a simple graph drawn in the plane, on points in
general position, with straight-line edges. We call \G a geometric realization
of the underlying abstract graph G. A geometric homomorphism from \G to \H is a
vertex map that preserves adjacencies and crossings (but not necessarily
non-adjacencies or non-crossings). Geometric homomorphisms can be used to
define a partial order on the set of isomorphism classes of geometric
realizations of an abstract graph G. In this paper, the homomorphism poset of
K_{3,3} is determined.
