Brickwork patterned parquet surprisingly gets its name from the way in which bricks are stacked.
Each block straddles the two blocks directly below and above, creating a pattern of shorter lines regularly intersecting perpendicular lines.
As with a basket weave pattern, the choice can be made of where the shorter line is in relation to the blocks above and below. You might choose to have it in the middle, as is more traditional, or you could stagger the blocks so they appear to be on one side or the other of blocks above and below.
An slightly more unusual pattern is the ladder pattern. This can be stunning with the right block and the right setting. However, this type of laying is to be approached with a bit of caution & preparation, as the blocks are not supported on all sides without false tongues in place.