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K846

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X(3), X(4), X(64), X(382), X(3357)

infinite points of the altitudes

ZaZbZc : pedal triangle of X(3357)

points of pK(X6, X382) on (O)

foci of MacBeath inconic : O, H and two imaginary

This cubic is related with Table 58. It is pK(X6, X382)'s sister. Its isogonal transform is K850 = spK(X382, X5).

K846 is the isogonal pK with pivot H with respect to the triangle Q1Q2Q3 whose vertices are the intersections of (O) and pK(X6, X382).

Since H is the midpoint of O-X382, it is X5 of Q1Q2Q3 hence K846 is the Napoleon cubic of Q1Q2Q3.

pK(X6, X382) and the decomposed cubic which is the union of (O) and the Euler line generate a pencil which contains K846 and the stelloid spK(X3, X4) = K525.