Watch this short video clip:
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Make a granny knot and a reef knot for yourself.
Now investigate their symmetries. Start with the granny knot.
Does it look the same after a half turn about a vertical
How about after a half turn about a horizontal axis from right to
Now try a half turn about a horizontal axis front to back. Does it
look the same this time?
(Don't forget you can play the video again to remind you of these
Try the same thing with a reef knot.
What is the same about the symmetries of the two knots?
What is different?