It is named after Walter Schnyder, who published its proof in 1989.
Schnyder's theorem states that a graph G is planar if and only if the order dimension of P(G) is at most three.
This theorem has been generalized by Brightwell and Trotter (1993, 1997) to a tight bound on the dimension of the height-three partially ordered sets formed analogously from the vertices, edges and faces of a convex polyhedron, or more generally of an embedded planar graph: in both cases, the order dimension of the poset is at most four.
However, this result cannot be generalized to higher-dimensional convex polytopes, as there exist four-dimensional polytopes whose face lattices have unbounded order dimension.
The incidence poset of a complete graph on n vertices has order dimension