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X(2), X(4), X(23), X(74), X(262), X(265) points at infinity of the McCay cubic K003 Y = X(15360) points of pK(X6, Y) on the circumcircle Z = X(15363) = X(4)X(265) /\ X(351)X(523) |
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Geometric properties : |
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Let Y = X(15360) be the intersection of the lines X(2)X(51), X(23)X(542), X(30)X(74), etc. K930 is the stelloid spK(X3, Q) where Q = X(15361) is the midpoint of X(3)-Y. See CL055. The three real asymptotes are parallel to those of the McCay cubic K003 and concur at X = X(15362), the homothetic of Y under h(X5, 1/3). K930 and pK(X6, Y) meet at Y, six points on the circumcircle and two other (not always real) points on the line X(3)Y. These points are isogonal conjugates and lie on K003. See the analogous cubic K669 where a generalization is given. The isogonal transform of K930 is K931, a CircumNormal spK. |