Are there examples of d-regular graphs (i.e. graphs where every node has exactly d adjacent nodes) which are not the 1-skeleton of a simple convex polytope?

UPDATE:

New version of the question: is there an example of a d-dimensional "simple" poset, i.e. a collection of k-dimensional "faces" with $k=0, 1, \dots, d$ equipped with partial ordering such that its 1-dimensional skeleton is a d-regular graph, which is not the face lattice of a convex polytope? (Obviously the partial order is to be interpreted as $X < Y$ if $X$ is contained in the boundary of $Y$).

It seems to be that the graph of the previous answer ($K_{3,3}$) cannot be interpreted as the 1-skeleton of a 3-dimensional simple poset.