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K617

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X(4), X(20), X(68), X(254), X(315), X(2996), X(3436), X(15454), X(15591), X(17732), X(34165), X(41361), X(43740), X(56683), X(56684), X(56685), X(56686), X(56687), X(56688), X(56689), X(56819), X(56872)

X(59422) → X(59436)

infinite points of the Orthocubic K006

points of pK(X6, X12111) on (O)

vertices of the antimedial triangle

K617 is an example of nodal cubic of Table 43. It is the cubic (K) obtained when P = X(20).

K617 has two nodal tangents at H parallel to the asymptotes of the Jerabek hyperbola and three asymptotes parallel to those of K006.

K617 is the anticomplement of the Lemoine cubic K009 and the isogonal transform of K389.

See K1347 for another locus property.

K260 is the locus of poles of all pKs having the same asymptotic directions as the Orthocubic K006. The locus of the pivots is K617 and the locus of the isopivots is K009.