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X(2), X(3), X(381), X(39641), X(39642)

X(39641), X(39642) are the imaginary foci of the Brocard inellipse, on the Brocard axis and the Kiepert hyperbola

infinite points of K003

foci of the Steiner inellipse

Q1, Q2, Q3 : vertices of the Thomson triangle

their reflections about X(2)

The Thomson cubic K002 and the focal cubic K463 generate a pencil of cubics passing through X(2), X(3), the four foci of the Steiner inellipse, the vertices Q1, Q2, Q3 of the Thomson triangle.

This pencil contains the central cubic K758 with center (X3), the central stelloid K833 with center (X2), the Thomson isogonal transform K727 of K833.

See Table 81 for general properties.