A planar graph is one which has a plane embedding. Two drawings are topologically isomorphic if one can be continuously deformed into the other. If we wrap a drawing onto a sphere, and then off again, we can move any face to be the exterior face.
We know the following theorem.
Theorem (Whitney) If $G$ is 3-connected, any two planar embeddings are equivalent.
My question is as the title says.
Is graph's planar embedding unique if each block of one planar graph is 3-connected?
Connectivity of the graph may even be one. I don’t know if there are any counterexamples or it may be true. Not sure if this is a proven fact.
PS: A block of a graph G is a maximal subgraph which is either an isolated vertex, a bridge edge, or a 2-connected subgraph.