The Origami Forum

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)?

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

Thanks for fixing it, Kafar! Can I post it on my website?

no problem, yes you can

PauliusOrigami wrote:Could you give me a reference (source)?

Also: http://dl.acm.org/ft_gateway.cfm?id=313 ... N=39024271

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)?

My understanding is that Maekawa's theorem and Kawasaki's theorem just tell you whether each vertex individually is flat-foldable or not. You can't have a flat-foldable crease pattern without satisfying both theorems at every vertex.

But just satisfying the theorems doesn't necessarily mean that the CP will be flat-foldable. Actually figuring out mathematically whether a CP is flat-foldable is much more complicated, not something that can be put into a simple set of rules.