I've discovered, that when you cut the 3-flip mobius strip down the middle, let it make 6 natural crossing when it wants to do, let the boundary cross itself to get a framed knot. Then draw the family of knot diagrams. The Jones Polynomail of the Mobius Knots equals the Jones Polynomial of the 3 band Siefert Surface when it is also cut down the middle avoiding the center of the disks. It also requires 6 crossings to make a frames knot and cancel the 8 twists. why is that? See my videos
