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X(2), X(15), X(16), X(511), X(7709), X(32442)

imaginary common points of Steiner ellipse and Lemoine axis (L)

X(32442) : intersection of Lemoine axis and line X(376)X(511)

intersections of (O) and line X(3)X(194)

Geometric properties :

K1099 is the Hessian cubic of the stelloid K1098 hence it is a focal cubic with singular focus X(7709). It is K048 in the ITB triangle mentioned at K1098.

K1099 is the locus of contacts of tangents drawn from X(7709) to the circles passing through X(15), X(16) hence orthogonal to the circumcircle (O) and more generally to any circle of the Schoute coaxal system.

One one these circles is the polar conic (C) of X(7709) in K1099.