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

X(4), X(5), X(143), X(14374), X(14375), X(14254), X(14632), X(14633) projections of X(5) on the altitudes infinite points of the McCay cubic 

This is a generalized Lemoine cubic as seen in the FG paper (See the Downloads page). It is the only cubic of this type which is a K60+ i.e. a stelloid. One group of pivots consists in X(5) (counted twice) and X(143). Its asymptotes are parallel to those of the McCay cubic and concur at X = X(13364), the homothetic of X(143) under h(X5, 1/3). It follows that any line passing through X meets K054 at three points whose isobarycenter is X. K054 is spK(X3, X12006) as in CL055 where X(12006) is the midpoint of X140X389. 
