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any suggestions for folding this tiling?

This tiling is really just causing me mental anguish. I’m trying to find an elegant way to fold it, and it’s just not happening so far.

strange tiling that is confusing me!
(click the photo for a larger version)

Totally open to suggestions or hints from crowd on this one. it’s really interesting looking, too… what I have folded so far is fascinating (to me, anyway). I’d really like to find a way to make it go the distance.

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