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X(1), X(3), X(4), X(1131), X(1132), X(1151), X(1152), X(5059)

Ua such that AUa = 5/2 AHa (vectors), Ub, Uc similarly

excenters

K156 is the member of the Euler pencil of isogonal pK whose pivot is P = X(5059) such that OP = -5 OH (vectors). See Table 27.

It has only one real asymptote which is parallel to that of the Soddy cubic K032.

K032 and K156 generate a pencil of cubics that contains the union of the line at infinity and the Kiepert hyperbola.