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X(80), X(2222)

K230 is an example of cK60+. See Special Isocubics ยง8.6.

It is an equilateral conico-pivotal cubic with root X(14628) on the lines X(57)X(655), X(80)X(497), X(224)X(514), X(312)X(1016), etc.

It has three concurring asymptotes at X(14629), the homothetic of X(2222) under h(X80, 1/3).

K230 is actually a nodal stelloid with pivots X(80) counted twice and X(2222). Hence, any circle through X(80) and X(2222) must meet K230 again at the vertices of an equilateral triangle.

More generally, any cK60+ must have its singularity on the tricircular sextic Q014.