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∑ SA^2 (y - z) y z = 0 or ∑ x (SC^2 y^2 - SB^2 z^2) = 0

X(2), X(69), X(1267), X(3926), X(5391), X(5490), X(5491), X(6337), X(6338), X(6339), X(6340), X(6341), X(6342), X(8222), X(8223), X(13430), X(13441)

vertices of the medial triangle

Geometric properties :

K1045 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, K1046, K1047.

K1045 is the image of the Thomson cubic K002 under the symbolic substitution SS{a -> SA}.

The barycentric product X(4) x K1045 is K170.

Note : this cubic is mentioned in ETC, article X(6337), with comments by Randy Hutson.