points at infinity of the Morley sidelines
their isotomic conjugates Ta, Tb, Tc
K089 is the singular isotomic nK60 with singularity at G. See Special Isocubics §7.3.3. K089 is a member of the class CL005 of cubics.
Its root is X(11055), the homothetic of X(76) under h(G,-3) hence K089 = nK(X2, X11055, X2).
K089 contains Ta, Tb, Tc, the isotomic conjugates of the points at infinity of the sidelines of the Morley triangle. TaTbTc is also an equilateral triangle inscribed in the Steiner ellipse. See "A Morley Configuration" in the Downloads page.
Compare K089 with K371 = pK(X2, X11055).