Hexa/tria lattice generation

How do we generate a regular hexagon / triangle combination of repeating cell geometry shown : (Plastic chair seat weave, Star of David).

Unlike a pure triangle lattice where a node has three intersecting lines this one has alternate sides disappearing when two lines intersect.

Can we modify this recent program? Recent Tria lattice generation

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Above base pattern is made in a mechanical software but is cumbersome.

Thanks for all help.