[qwibqklp] Tessellating space with 2x3 Lego bricks

Place 6 2x3 Lego bricks next to each other so they form a 6x6 square.  Place squares next to each other alternating orientations in a checkerboard pattern.  The next layer of squares goes on top, with the center of each square going above the corners of the layer below.

The third layer faces a decision: whether the orientation of the 2x3 bricks in a square should be the same as, or perpendicular to, the orientation of the square two layers below.

I think this decision is isomorphic to the face centered cubic versus hexagonal close packing of spheres.

Practically this decision causes the difficulty of consistently creating this tessellation when a layer must be consistent with a now-covered layer two layers below.  There also exist some deep seams and weakly connected sections.

I don't think there's a decision to be made about the second layer; either decision results in the same tessellation, perhaps rotated.