In other words, can anyone give an example of a tricolourable knot that is equivalent under the Reidemeister moves to its mirror image? If not, is it known or conjectured anywhere in the literature that no tricolourable knot is equivalent under the Reidemeister moves to its mirror image?
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3$\begingroup$ Square knot is amphichiral and tricolorable. Perhaps for prime knots the answer is positive though. $\endgroup$– WojowuCommented Oct 14, 2020 at 11:45
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3$\begingroup$ KnotInfo has lots of prime examples -- look at determinant and symmetry type, and anything with det(K) a multiple of 3 and amphichiral symmetry will work. The first of these is 8_18. $\endgroup$– Steven SivekCommented Oct 14, 2020 at 12:29
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1$\begingroup$ Thank you both! $\endgroup$– user166980Commented Oct 14, 2020 at 12:39
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