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X(2), X(4), X(13), X(14), X(542), X(868), X(9140)

two imaginary points S1, S2 on the Kiepert hyperbola, the orthocentroidal circle, the line X(115)X(125)

Q = reflection of X(4) in the line X(115)X(125), SEARCH = 7.59482985519816

See Table 59 for other similar cubics and a generalization.

K873 is an axial focal cubic with

• axis the line X(115)X(125), the perpendicular bisector of the Fermat points X(13)X(14).

• singular focus X(868), the intersection of this same line and the Euler line. The polar conic of X(868) is the circle passing through X13, X14, X868, X1316, X1640.

• orthic line the Fermat axis.

• asymptote the image of the Fermat axis under the homothety with center X(868), ratio 2.

K876 is the other cubic of the pencil described in Table 59 having the same circular polar conic.