10 124 Quick Notes

10_124 is also known as the torus knot T(5,3) or the pretzel knot P(5,3,-2). It is one of two knots which are both torus knots and pretzel knots, the other being 8_19 = T(4,3) = P(3,3,-2).

It seems like the prior statement is incorrect. I suspect what this should say is 10_124 and 8_19 are the only torus knots which are also almost alternating. See page 108 in the Encyclopedia of Knot Theory. Confirmation of this is that 3_1 is the pretzel knot P(1,1,1), i.e., the right-handed trefoil. It looks like 5_1 is a pretzel knot also, and so on, i.e. 7_1, 9_1, and should include the Hopf link and the Solomon link etc. These are torus knots/links also.