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

too complicated to be written here. Click on the link to download a text file.

X(2), X(76), X(850), X(2592), X(2593), X(3413), X(3414), X(15164), X(15165)

isotomic conjugates of X(1113), X(1114)

inf3 = X(523) x X(183), the third point at infinity

Geometric properties :

The McCay cubic K003 is a stelloid hence it has three concurring asymptotes (at the centroid G of ABC).

A multiple of K003 is the barycentric product of K003 by a certain point P. It is the pivotal cubic (K) = pK(X6 x P^2, X3 x P) but this cubic doesn't necessarily have concurring asymptotes unless P lies on K1070.

K1070 has three real asymptotes : two are the parallels at X(76) to those of the Kiepert hyperbola and one is the parallel at X(7757) to the line passing through X(2), X(647) with infinite point inf3 as above.

It follows that the polar conic of X(76) must be a rectangular hyperbola (H) which contains X(2), X(76), X(316), X(325), X(850), X(3413), X(3414) and also the tangential X of inf3.

Examples :

• when P = X(2), (K) is obviously K003 itself and when P = X(76), (K) is pK(X76, X69) which is actually the isotomic transform of K003, also the barycentric quotient of K003 by X(6).

• when P = X(850), (K) is pK(X338, X525). See the related K1071.