Lattice hexa/tria generation – Mathematica Stack Exchange

How to generate a regular hexagon / triangle combination of cell geometry shown : (Plastic chair seat weave, Star of David) lattice. Unlike a pure triangle lattice , anode has three intersecting lines this one has alternate scheme with two lines intersecting, alternate line is deleted.

How can we modify here? Recent Tria lattice generation

enter image description here

Above pattern is made in a Mechanical software but is quite cumbersome.

Thanks for all help.