We choose the origin for x at one of the points of reflection. Now all reflections which map the pattern to itself are of the form a − x where the constant " a " is an integer (the increments of a are 1 again, because we can combine a reflection and a translation to get another reflection, and we can combine two reflections to get a translation). Therefore all isometries can be characterized by an integer and a code, say 0 or 1, for translation or reflection.