Home page  Catalogue  Classes  Tables  Glossary  Notations  Links  Bibliography  Thanks  Downloads  Related Curves 

X(2), X(6), X(599) foci of the Steiner inellipse, see also Table 48. points at infinity of the Grebe cubic K102 common points of the circumcircle and pK(X6, X599) 

The Thomson cubic K002 and the Brocard (second) cubic K018 are both isogonal isocubics which pass through G, K and the (four) foci of the Steiner inellipse. Hence they generate a pencil of circumcubics through the same points. This pencil contains K287, a central K++ with center G and also K353. The three asymptotes are the parallels at G to those of the Grebe cubic K102. It meets the circumcircle at the same points as pK(X6, X599). K287 is spK(X6, X2) in CL055. Its isogonal transform is K729 = spK(X599, X2). 
