A partially ordered set P is called a k-sphere order if one can assign
to each element a is-element-of P a ball B(a) in R(k) so that a < b i
ff B(a) subset-of B(b). To a graph G = (V, E) associate a poset P(G) w
hose elements are the vertices and edges of G. We have v < e in P(G) e
xactly when v is-an-element-of V, e is-an-element-of E, and v is an en
d point of e. We show that P(G) is a 3-sphere order for any graph G. I
t follows from E. R. Scheinerman [''A Note on Planar Graphs and Circle
Orders, '' SIAM Journal of Discrete Mathematics, Vol. 4 (1991), pp. 4
48-451] that the least k for which G embeds in R(k) equals the least k
for which P(G) is a k-sphere order. For a simplicial complex Kone can
define P(K) by analogy to P(G) (namely, the face containment order).
We prove that for each 2-dimensional simplicial complex K, there exist
s a k so that P(K) is a k-sphere order.