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The Darboux cubic K004 and the Lucas cubic K007 generate a pencil of cubics passing through A, B, C, H, L = X(20) and the four CPCC points, see table11.
This pencil contains several remarkable cubics mentioned in the following table.
other centers Xi for i =
see the page
one of the three pK of the pencil, a pK++
one of the three pK of the pencil
also member of the pencil K005 - K060
the only equilateral cubic of the pencil, a K60+
the only circular cubic of the pencil
one of the three pK of the pencil, a pK+