Space Groups
The space groups in two dimensions are called wallpaper groups. In three dimensions, the space groups are the symmetry groups
possible in a crystal lattice with the translation symmetry element. There are 230
space groups in
, although 11 are mirror
images of each other. They are listed by Hermann-Mauguin
symbol in Cotton (1990).
SEE ALSO: Crystallographic Point Groups,
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, pp. 248-249,
1985.
Bülow, R.; Neubser, J.; and Wondratschek, H. "On Crystallography in Higher Dimensions. II. Procedure of Computation in
." Acta
Cryst. A 27, 520-523, 1971.
Brown, H.; Blow, R.; Neubser, J.; Wondratschek, H.; and Zassenhaus, H. Crystallographic
Groups of Four-Dimensional Space. New York: Wiley, 1978.
Buerger, M. J. Elementary
Crystallography. New York: Wiley, 1956.
Burgbacher, F.; Laemmerzahl, C.; Macias, A. "Is There a Stable Hydrogen Atom
in Higher Dimensions?" J. Math. Phys. 40, 625-634, 1999.
Cotton, F. A. Chemical Applications of Group Theory, 3rd ed. New York: Wiley, pp. 250-251,
1990.
Hermann, C. "Kristallographie in Räumen beliebiger Dimensionszahl. I. Die
Symmetrieoperationen." Acta Cryst. 2, 139-145, 1949.
Neubser, J.; Wondratschek, H.; and Bülow, R. "On Crystallography in Higher Dimensions. I. General Definitions." Acta Cryst. A 27, 517-520,
1971.
Opechowski, W. Crystallographic
and Metacrystallographic Groups. Amsterdam, Netherlands: North-Holland, 1986.
Rabson, D. A.; Huesman, J. F.; Fisher, B. N. "Cohomology for
Anyone." Found. Phys. 33, 1769-1796, 2003.
Schwarzenberger, R. L. E. "Classification of Crystal Lattices."
Proc. Cambridge Philos. Soc. 72, 325-349, 1972.
Schwarzenberger, R. L. E. "Crystallography in Spaces of Arbitrary
Dimension." Proc. Cambridge Philos. Soc. 76, 23-32, 1974.
Strebel, R. "Burckhardtsche Bestimmung der Raumgruppen I." Elem. Math. 58,
141-155, 2003.
Wondratschek, H.; Bülow, R.; and Neubser, J. "On Crystallography in Higher Dimensions. III. Results in
." Acta
Cryst. A 27, 523-535, 1971.
Referenced on Wolfram|Alpha:
Space Groups
CITE THIS AS:
Weisstein, Eric W. "Space Groups." From
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