Space Groups

The space groups in 2-D are called Wallpaper Groups. In 3-D, the space groups are the symmetry Groups possible in a crystal lattice with the translation symmetry element. There are 230 space groups in $\Bbb{R}^3$, although 11 are Mirror Images of each other. They are listed by Hermann-Mauguin Symbol in Cotton (1990).

See also Hermann-Mauguin Symbol, Lattice Groups, Point Groups, Wallpaper Groups

References

Arfken, G. ``Crystallographic Point and Space Groups.'' Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 248-249, 1985.

Buerger, M. J. Elementary Crystallography. New York: Wiley, 1956.

Cotton, F. A. Chemical Applications of Group Theory, 3rd ed. New York: Wiley, pp. 250-251, 1990.