Given a set of face cycles computed from a planar embedding (consisting of a clockwise ordered adjacency list for each vertex in a connected graph component), is it possible to determine the unbounded face?

Visually it's easy to confirm since the unbounded cycle will be traversed on the opposite clockwise direction as the remaining cycles. But in terms of moving from one edge to the next in the unbounded face, the edge selection conforms to the same clockwise ordering as the remaining faces in the embedding.