Specifically:

Razzmatazz wrote:Determining if it is flat fold-able via Maekawa's and Kawasaki's theorem has been disproven. However it is a good general rule.

And latter Razzmatazz was asked to provide evidence:

PauliusOrigami wrote:Razzmatazz wrote:Determining if it is flat fold-able via Maekawa's and Kawasaki's theorem has been disproven. However it is a good general rule.

Could you give me a reference (source)?

But Razzmatazz's answer is based on an article that to be read needs to be purchased first:

Razzmatazz wrote:Apparently the proof is in this document: http://dl.acm.org/citation.cfm?id=313852.313918

But it is in the wikipedia article for Kawasaki's theorem here: http://en.wikipedia.org/wiki/Kawasaki%27s_theorem

So does anyone have more information on said exceptions/disproval?