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K1201

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X(2), X(6), X(13), X(14), X(15), X(16), X(17), X(18), X(19106), X(19107), X(23249), X(23259)

X(42522) → X(42533)

Q1, Q2 below

Geometric properties :

K1201 is a KHO-cubic. See K1191 for explanations and also CL075.

Its KHO-equation is : x^2(9y - 2z) - (2y - z)(6y^2 + 11yz + 2z^2) = 0.

Points on K1201 :

Q1 = (3, 2, -11) = 13 a^4-11 a^2 b^2-2 b^4-11 a^2 c^2+4 b^2 c^2-2 c^4 + 2√3 S a^2 : : , on the lines {X3,X13}, {X16,X376}, {X18,X20}, {X62,X548}, SEARCH = 21.4411313302830.

Q2 = (3, -2, 11) = 13 a^4-11 a^2 b^2-2 b^4-11 a^2 c^2+4 b^2 c^2-2 c^4 - 2√3 S a^2 : : , on the lines {X3,X14}, {X15,X376}, {X17,X20}, {X61,X548}, SEARCH = 6.40439060053309.

K1201 meets the Euler line at X(2) and two other points with KHO-coordinates (9√3, 2, -23) and (9√3, -2, 23).