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X(1), X(9), X(19), X(40), X(57), X(63), X(84), X(610), X(1712), X(2184) excenters 

The hexyl triangle is the reflection in O of the excentral triangle IaIbIc. See also TCCT p.172. The locus of P whose anticevian or antipedal triangle is perspective to the hexyl triangle is K343. In the anticevian case, the locus of the perspector is the Darboux cubic. In the antipedal case, the locus of the perspector is a complicated sextic passing through X(1), X(3), X(40). K343 is anharmonically equivalent to the Thomson cubic. See Table 21. 
