Most symmetric unit cell in a two-dimensional arrangement Consider the two dimensional structure below, where two atoms A (white) and B (black) are displayed like a brick wall.

I need to find the most symmetric primitive unit cell of this structure and the unit vectors of this cell. The most symmetric primitive unit cell (I think) I could find was a square with alternating atoms at its vertices, but I noticed that this is not invariant under a translation of $\Delta$.

The other unit cell was a rectangle, following the "bricks", but this one is not primitive.

What am I doing wrong here?
 A: When faced with a repeating pattern, the conceptual issue is to identify the underlying Bravais lattice and a possible basis to describe the crystalline structure. Of course, there are many (infinite) possibilities for these elements. Still, the constraint of having the minimal basis and the most symmetric primitive unit cell for the Bravais lattice are good guidelines.
The presence of two differently colored circles and only a single pattern of "bonds" around each of them (all the white circles have bonds in the WNE directions, while all the black circles have bonds in the ESW directions) suggest the possibility of a minimal two-atom basis.
The search for the Bravais lattice is quite simple. One can start from a circle of a given color. Then one has to look for the minimum displacements in two linearly independent directions, bringing to a circle of the same kind and having the same kind of environment.
In this case, for example, any pair of non-aligned displacements from a black circle to another black circle would be fine. However, there is a straightforward and symmetric choice, as indicated in the following figure. To the best of my ability to measure distances, it looks like a square, a highly symmetric choice.

With such a choice, the basis is made by any pair of two atoms of a different color.
