Despite similar looks, this tessellation is not Momotani’s Wall — it is a different pattern designed by myself. Its relation to Momotani’s Wall is roughly such as the relation of Pythagorean Tiling to Rectangle and Square Flagstone.
The twists being placed around the rectangle with rotational but without axial symmetry lead to some interesting properties. First, the tessellation is not rectangular, although the staggered rectangles create a roughly rectangular outline whose sides are not parallel to the sides of the bricks. Second, unlike Momotani’s Brick Wall, the bricks in this design can be made with different proportions. The height is always two grid units and the length can be arbitrary as long as it’s at least two grid units. In this fold, the proportions are 3:2. The case with square bricks is the same design as Pythagorean Tiling with 1:1 ratio and the way I came up with the idea for Shifted Bricks was by modifying that model. It is even possible to mix different brick lengths in a single model as long as the length is consistent along each strip of bricks whose top and bottom edges are adjacent.
Shifted Bricks is an iso-area tessellation. In contrast to Momotani’s Wall, the bricks on both sides are parallel rather than perpendicular to each other. The direction of the slant between brick columns is mirrored between the sides. In the pictures you can see that I folded the model in such way that the front side is completely clean while the back side has some visible construction creases. Folding both sides cleanly seems possible for but rather tedious for larger grids (the model shown here is from 32×32 grid).
I will be teaching this model at the online CDO convention this November.