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The points Ωa, Ωb, Ωc are the only points for which there are infinitely many equilateral pKs with pole one of these points. They lie on a large number of curves although they are not constructible with ruler and compass only. See also CL052 and Table 18. Conics Two conics 

These three points lie on two conics (C1) and (C2) that meet at a fourth point Z, intersection of the lines X(5)X(1989) and X(6)X(30). (C1) contains X(6), X(53), X(216) and X(1989). (C2) contains X(395), X(396), X(523) and X(3003). 



Cubics These points Ωa, Ωb, Ωc lie on the PΩe–transforms of all the cubics that pass through the points Ua, Ub, Uc of Table 18. The following table gives a selection of these cubics. 




