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X(1), X(2), X(8), X(9), X(144), X(165), X(210), X(518), X(3057), X(3307), X(3308), X(15587), X(24646), X(24647) isogonal conjugates in (T) below of X(210), X(24646), X(24647) 

Geometric properties : 

K1084 is the SS{X188}, SS{X9}, SS{X366} image of K907, K1083, K1085 respectively. See Table 70 and also Table 62. SS{X9} actually swaps K1083 and K1084. This transformation can be seen as the oblique symmetry with axis the line X(2)X(11) and direction the line X(1)X(9)X(518). These two cubics are members of a pencil of cubics which contains the union of the line at infinity, the lines X(1)X6)X(9) and X(2)X(11). All these cubics are isogonal pKs in a non proper triangle (T) with vertices X(518), X(24646), X(24647). See K1083 for further details. Note that the pivots of K1083 and K1084 are X(354) and X(210) respectively. These points are symmetric about X(2).


