X(4), X(13), X(14), X(30), X(113), X(1300)
vertices of the orthic triangle
O(X4) is the orthopivotal cubic with orthopivot H. See the FG paper "Orthocorrespondence and orthopivotal cubics" in the Downloads page and Orthopivotal cubics in the glossary. See also K295 and K001, property 3.
It is the circular pK with pivot H and pole X(1990), intersection of the orthic axis and the line HK. Its singular focus is X(125). Its orthic line is the Euler line.
It is the anti-orthocorrespondent of the Kiepert hyperbola.
The isogonal transform of K059 is K114.