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X(4), X(140), X(550)

points at infinity of the Napoleon cubic K005

X5-OAP points, see Table 53

reflections of A, B, C about X(140)

other points below

K821 is a central cubic with center X(140) that passes through the four X5-OAP points. These points lie on the stelloid K665 and on a rectangular hyperbola (H) passing through X(140), X(550) and homothetic to the Jerabek hyperbola.

K821 meets K005 at three points on the line at infinity and six other finite points namely A, B, C, H, Q1, Q2. These two latter points are the common points of the line X(140)X(195) and the circum-rectangular hyperbola (H') passing through X(549). Their midpoint is obviously X(140).