This is the first group that contains glide reflections. A fundamental region for the translation group is a rectangle, and one can be chosen that is split by an axis of reflection so that one of the half rectangles forms a fundamental region for the symmetry group. There are neither rotations nor glide reflections. The axes of reflection are parallel to one axis of translation and perpendicular to the other axis of translation. This is the first group that contains reflections. A fundamental region for the symmetry group is half of a parallelogram that is a fundamental region for the translation group. The two translations axes may be inclined at any angle to each other. As in all symmetry groups there are translations, but there neither reflections nor glide reflections. Rotations, that is, rotations of order 2.
This group differs only from the first group in that it contains 180° Is parallelogrammatic, so a fundamental region for the symmetry group is the same as that for the translation group, namely, a parallelogram. Translation axes may be inclined at any angle to each other. There are neither reflections, glide-reflections, nor rotations. International Union of Crystallography in 1952. The IUC notation is the notation for the symmetry group adopted by the * = not all rotation centers on reflection axes + = all rotation centers lie on reflection axes There are enough characteristics listed in the table to distinguish the 17 different groups. Note that clicking on a small image below will take you to a discussion of the associated symmetry group (as will selecting the name of the group in the headings below).Ī short table of characteristics of the symmetry groups
A mathematical analysis of these groups shows that there are exactly 17 different plane symmetry groups. The various planar patterns can by classified by the transformation groups that leave them invariant, their symmetry groups. Wallpaper Groups: the 17 plane symmetry groups The 17 plane symmetry groups