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Knot Theory… Question in comments

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So looking at this post of this weird throw pillow thing made me wonder. It’s clearly a Variant of the Tresfoil knot, but I’m not sure how to describe it.

First of all, I’m not entirely sure what kind of variant is it: is it two loops operating in parallel or one loop that follows the same path twice?  That probably can’t be answered just from a picture, although it does look like one process in front of the other at one point, so maybe it’s one loop?

But how would you describe those two types of knots? How would it affect their invariants? (I’ve never had a class in l not theory, but it’s kind of cool and I’m just wondering.)

I’m not sure why this is Marked resolved. It’s not resolved.
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Certainly knot the most comfortable pillow :)
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I’m still curious about this. I looked up parallel nuts, but that’s not it. It seems that there should be a specific category for two loops in the same formation and also for one not that kind of goes around twice.

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