Left trefoil	Right trefoil

Left trefoil and Right trefoil are mirror images to each other.

Polynomial is the only invariant that we can prove they are different.

Name	Figure	Jones Polynomial
Left trefoil		-1/t4 + 1/t3 + 1/t
Right trefoil		t + t3 - t4

Polynomial: 1/t² - 1/t + 1 + t + t²

This one is "symmetric".

Figure	Jones Polynomial
	-1/t3 - 1/t2 + 2/t -3 + 3t - 3 t2 +3 t4 - 2 t2 + t5
	-1/t +2 -t +2 t2 -t4 + t2 -t5
	1/t7 - 2/t6+2/t5 - 3/t4 +3/t3 - 2/t2 + 2/t
	-1/t8 + 1/t5 +1/ t3

• 1929 J. Alexander
• 1958 Conway-Alexander
• 1984 Vaughan Jones
• then many others