The Origami Forum

I remembered having read about Maekawa's theorem about flat foldability on an inner vertex being disproved but I could not remember where but finally I found what thread it was, it is this one: viewtopic.php?f=16&t=12181&p=132045

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?

I remember finding a presentation online (unfortunately, I can’t remember where) that touched on the (dis)proof of the theorems, giving crease patterns of a couple counterexamples. I have it saved on my computer, however; so maybe I can send it to you. (This assumes that I’m thinking of the right one.)
As far as I can remember, it has something to do with the law of origami that a sheet can’t intersect itself. In essence, two vertices that would ordinarily fold flat on their own may not fold flat together if they’re too close on the paper.

Thank you Balton, I'll PM you my email address