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This is exactly what you think it is:  a zipper that is also a Mobius strip. The cool part is that you can play around with splitting the strip down the middle, since you can't un-cut a paper Mobius strip but you can un-unzip (commonly known as "rezipping" or simply "zipping") a zipper.

Video!

Materials:
A zipper: make sure you get the kind that splits into two halves, not the kind that stays together. I got em at SCRAP.

Tools:
Needle & thread. Or a sewing machine.

Step 1: Sew the Zipper Together

Just take the zipper and make a Mobius strip with it, sewing the ends together. Not really that much to say here. Don't sew the two halves of the zipper together.

You can also take multiple zippers and sew them together next to each other, and make something you can split multiple times!

Now you're done. Go play with it!
That is pretty cool. hehe nice!

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