Thus spake "Origami on behalf of Jorge E. Jaramillo" 
< on behalf of> on 
7/28/19, 3:35 PM:

    I think I remember having read somewhere that Maekawa's theorem about the 
flat foldability of the creases at a vertex having a difference of +-2 between 
mountains and valleys has exceptions but I've never come across any of them, 
except for vertices on edges.
    So is it true about the exceptions?

Maekawa's Theorem applies only to vertices in the interior of a crease pattern, 
and only applies to flat-foldable patterns.
    Also, is there a theorem about edge vertices?

There are theorems about edge vertices, but not ones that relate to the number 
of mountain and valley folds. It's easy to construct an edge vertex with any 
given number of valleys and mountains.


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