The Foosball symmetry group. Symmetry Group P2 is based on a four sided grid, which can be skewed into lozenges, parallelograms. Each of the corners has a two-fold rotation point.
This is another favourite symmetry group. The characters are all arranged side by side, with every other one flipped, like on a skewer. Or a series of foosball players, alternated heads up, heads down, along a series of parallel bars.
This post is the second in a series of 17, as there are 17 symmetry groups that tile the two dimensional surface, aka, the plane.