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∑ a^4 SA^2 (c^2 y - b^2 z) y z = 0

X(3), X(6), X(394), X(493), X(494), X(1124), X(1335), X(3167), X(6391), X(6461), X(10665), X(10666)

vertices of the cevian triangle of X(6)

Geometric properties :

K1047 is an example of pK anharmonically equivalent to the Orthocubic K006.

Other examples : K070a, K070b, K168, K170, K171, K233, K424a, K424b, K678, K707, K857, K1039, K1045, K1046.

K1047 is the isogonal transform of K1046, also the barycentric product X(6) x K1045.

K1047 is the image of K1312 = pK(X1500 = X37^2, X10) under the symbolic substitution SS{a -> SA}.

Note that pK(X37^2, X10) is the barycentric product X(10) x K002. It is the locus of the pseudo-isopivots of central cubics psK with center X(10).

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K1313 = pK(X14575, X6) is the locus of the pseudo-poles of central cubics psK with center X(6).

The loci of the pseudo-pivots and the pseudo-isopivots are K233 and K1047 respectively.

See Pseudo-Pivotal Cubics and Poristic Triangles and Central cubics.