What is the best tying material to use? If yarn, what type?

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Sometimes if it is hand sewn, then you would have to knot it. If you keep going through the front, it'll be loose. You knot it and if you still...

Any sort of medium to heavy duty fabric should work - it needs to be stiff enough to hold the shape of the hat. So something like cotton, canvas or...

Yes, any kind of yarn should work fine.

There is not one material that is best - hardwood floors, tile, and vinyl all work great. The choice is mostly dependant on your budget.