To make the shape in an old fashioned silly way, you may (Smart Guides are your friends):
1) Create a hexagon with the Polygon Tool and rotate it to have vertical sides;
2) Move a copy vertically up by 3/4 of the height (or 1.5 times the radius when creating it), then create a circle concentric with the original hexagon and extending past the copy;
3) Rotate copies of the copy hexagon and the circle twice by 120 degrees;
4) Delete the circles, select all hexagons, and Pathffinder>Divide;
5) Ungroup and delete everything outside the innermost shape;
Now you just need the inner lines:
6) With the Line Tool drag from each outer corner to opposite inner corner (Smart Guides say anchor);
7) Select each line, click at the centre with the Scissors Tool (Smart Guides say intersect), and delete the short end, then Group everything.
Having done all of what Jacob says, repeat your thingummy like this (left):
Draw a no-fill no-stroke rectangle as per the dashed line. Move it a bit (centre) to avoid splitting strokes in half (if your thingummy is stroked).
Send the rectangle to back and drag the whole thing to the Swatches panel. And there’s your pattern (right).
Very nice, Steve (it was too late to even think of 2), just unable to resist 1) as a nightcap).