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X(6), X(2420) upto X(2445) 

K162 is the isogonal transform of the Simson cubic K010. It is a conicopivotal cubic with singularity X(6) and root X(3). See Special Isocubics ยง8. The three real inflexions lie on the trilinear polar of X(54). See K406 for a generalization. 
