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Dot patterns

For the hexagonal pattern the counts are hexagons, not dots — the dots sit on their vertices.
Dots on the vertices of a square, triangular or hexagonal lattice. Spacing is the center distance between neighboring dots. Give either the area to fill (as many dots as fit, centered) or exact dot counts (the area follows). Dots can be cut outlines (drill holes) or filled circles (engraving). The pattern is centered inside the optional box.