The Seventeen Groups
Each of the groups in this section has two cell structure diagrams, which are to be interpreted as follows:
| a centre of rotation of order two (180°). | |
| a centre of rotation of order three (120°). | |
| a centre of rotation of order four (90°). | |
| a centre of rotation of order six (60°). | |
| an axis of reflection. | |
| an axis of glide reflection. |
On the right-hand side diagrams, different equivalence classes of symmetry elements are colored (and rotated) differently.
The brown or yellow area indicates a fundamental domain, i.e. the smallest part of the pattern that is repeated.
The diagrams on the right show the cell of the lattice corresponding to the smallest translations; those on the left sometimes show a larger area.
Read more about this topic: Wallpaper Group
Famous quotes containing the words seventeen and/or groups:
“It was not sufficient for the disquiet of our minds that we disputed at the end of seventeen hundred years upon the articles of our own religion, but we must likewise introduce into our quarrels those of the Chinese. This dispute, however, was not productive of any great disturbances, but it served more than any other to characterize that busy, contentious, and jarring spirit which prevails in our climates.”
—Voltaire [François Marie Arouet] (1694–1778)
“Belonging to a group can provide the child with a variety of resources that an individual friendship often cannot—a sense of collective participation, experience with organizational roles, and group support in the enterprise of growing up. Groups also pose for the child some of the most acute problems of social life—of inclusion and exclusion, conformity and independence.”
—Zick Rubin (20th century)