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.