  A classic theorem by Steinitz states that a graph G is realizable by a convex
polyhedron if and only if G is 3-connected planar. Zonohedra are an important
subclass of convex polyhedra having the property that the faces of a zonohedron
are parallelograms and are in parallel pairs. In this paper we give
characterization of graphs of zonohedra. We also give a linear time algorithm
to recognize such a graph. In our quest for finding the algorithm, we prove
that in a zonohedron P both the number of zones and the number of faces in each
zone is O(square root{n}), where n is the number of vertices of P.
