= Extrusion invariance of a ternary triangular scheme
{title2=$b_j=\sum_{i\equiv0\ (\mathrm{mod}\ 3)}a_{i,j}=\sum_{i\equiv1}a_{i,j}=\sum_{i\equiv2}a_{i,j}$}
If a triangular-lattice <subdivision mask> has the displayed residue-sum equality, refining data $p_{i,j}=q_j$ gives $p'_{I,J}=\sum_k b_{J-3k}q_k$, independent of $I$. If affine coordinates reproduce their parameter positions, a geometrically straight extrusion is preserved. Rotationally symmetric masks give the corresponding property in all three lattice-edge directions. A boundary curve compatible with this extrusion uses the collapsed mask $b$, not just the central row of the two-dimensional mask.
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