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X(1), X(2), X(7), X(57), X(145), X(174), X(1488), X(2089) infinite points of the Thomson cubic. vertices of the intouch triangle 

K365 is a member of the classes CL040 and CL042. It has three real asymptotes parallel to those of the Thomson cubic. The isogonal transform of K365 is K761 = pK(X41, X1) and its isotomic transform is pK(X312, X75). 
