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X(4)

foci of the Johnson circum-conic

infinite points of the McCay cubic K003

K714 is a circum-cubic that passes through the foci of the circum-conic (C) with center X(5), perspector X(216). (C) is sometimes called the Johnson circum-conic and it contains the vertices of the Johnson triangle, the reflection of ABC about X(5).

K714 is a stelloid. Its asymptotes are parallel to those of the McCay cubic K003 and concur at X = X(14640).

K714 meets :

• the line at infinity at the same points as K003 and also K096 = pK(X216, X20),

• the circum-conic (C) at the same points as pK(X216, X5562).

K714 is also a member spK(X3, Q) of CL055 with a complicated corresponding point Q.