= Cubic propagation along a triangular strip
{title2=$i+j+k=0$}
A two-cell-thick strip of triangles with degree-six vertices in a <dual arrangement of a planar point set> produces three indexed primal point families with collinearities $a_i,b_j,c_k$ whenever $i+j+k=0$. A <plane cubic> can be fitted to nine initial points because its homogeneous coefficient space has dimension ten. Overlapping nine-point configurations then force each next point onto the same cubic by <eight-point cubic completion for two triples of lines>. Safe neighbourhoods guarantee the distinctness needed in these local completion steps. A possible seed is $a_{-1},a_0,a_1,a_2,b_{-3},b_{-2},b_{-1},c_1,c_2$. Adjacent completion blocks force $c_3,b_{-4},c_4,a_{-2}$, followed by the alternating continuation along the two long transverse families.
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