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X(2), X(182), X(4550), X(7709)

infinite points of K003

vertices of the CircumNormal triangle N1N2N3

vertices of the CircumTangential triangle T1T2T3

Geometric properties :

K1290 is an equilateral cubic having three axes of symmetry parallel at O to the sidelines of the CircumNormal and CircumTangential triangles. See Table 25.

It is therefore invariant under the rotations with center O and angles ±2π/3.

It is also invariant under the products of isogonal conjugations with respect to the CircumNormal and CircumTangential triangles.

Each conjugation transforms K1290 into the same cubic which turns out to be the reflection of K1290 in O. This is also an equilateral trefoil of the same type which passes through X(376), X(3098), X(6194), X(8717) and obviouly the points of K1290 on the line at infinity and on (O).