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A cubic is a member of the Steiner net when it is a circumcubic passing through the (four) foci of the Steiner inscribed ellipse, the inconic with center the centroid G of ABC. Any such cubic is a spK(P, G) for some P. See CL055 for general properties of these cubics and their construction. The following table gives a selection of spK(P, G) according to P. 



Notes : • spK(P, G) is circular if and only if P lies at infinity, giving a pencil of focal nKs with root G, focus F on (O), see yellow lines. • spK(P, G) is also a nK when P lies on the Steiner (circum) ellipse in which case its root lies on this same ellipse and the pole on K229. Two examples are given in the pink lines. • spK(P, G) is a K0 if and only if P lies on the line GK in which case it contains G and K, see red points P in the table. • if P and P' are symmetric about G then the cubics spK(P, G) and spK(P', G) are swapped under isogonal conjugation. They meet again at two isogonal conjugate points on K002 hence collinear with G. 
