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The thumbnail shows a hexagonal tiling, which is like a brick-laying pattern but rotated 90 degrees, so the "half bricks" are on the top and bottom, not the sides.
Maybe it would still work to orient the hexagons so the zig-zag part is on the walls, and then fill in the gaps with half-height half-width walls. Although "half" isn't exactly correct; the hexagons give you ugly trig numbers.
You don't need any ugly trig. You can just use a magic number. The magic number in question is 0.8660254, which is the ratio between the width of the longways (point-to-point) to shortways (flat-to-flat) dimensions of a regular hexagon. If you need half of that, divide it by 2 afterwards.
magic ⇏ ¬ugly