# Finding a 2-connected planar graph

Find a 2-connected planar graph whose drawings are all topologically isomorphic, but whose planar embeddings are not all equivalent.

I think $K_{2,3}$ might be an example, but I'm not sure how to show this at all. Anything would be welcome.

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This sounds like homework, so I will give you a hint. The graph you are looking for must be 2-connected but not 3-connected. Thus, it must have two vertices whose removal disconnects the graph. Try drawing different graphs like this -- you will need something more complicated than $K_{2,3}$ to get the job done. – Jim Belk Feb 8 '11 at 1:37
Like K_{2,4} or something? – user6584 Feb 8 '11 at 9:11