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March 10, 2020

Sketch of proof that the trefoil is unequal to it’s mirror image.

Filed under: clarification of demonstration — Rob @ 8:28 am
The top diagram shows that the reduced diagram of the trefoil must take the shape that it does as well as being knotted through the use of tricolorability as shown in the previous entry. The doublets a(1)r(1), b(1)s(1),,, etc. are shown as a(1), a(2), etc. and have the same cyclic order as from when the knot diagram is first reduced. If I don’t consider knot direction then either the left hand or the right hand trefoil can be reformed but if I give the knot a direction then only the original handedness can be recovered.

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